CBSE Class 12 Mathematics Application Of Integrals Worksheet Set A

Read and download free pdf of CBSE Class 12 Mathematics Application Of Integrals Worksheet Set A. Students and teachers of Class 12 Mathematics can get free printable Worksheets for Class 12 Mathematics Chapter 8 Application Of Integrals in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 12 students should practice questions and answers given here for Mathematics in Class 12 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 12 Mathematics Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

Worksheet for Class 12 Mathematics Chapter 8 Application Of Integrals

Class 12 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 8 Application Of Integrals in Class 12. This test paper with questions and answers for Class 12 will be very useful for exams and help you to score good marks

Class 12 Mathematics Worksheet for Chapter 8 Application Of Integrals

Question. The area (in sq. units) of the region {(x, y) : 0 ≤ y ≤ x2 + 1, 0 ≤ y ≤ x + 1, 1/2 ≤ x ≤ 2) is :
(a) 23/16
(b) 79/24
(c) 79/16
(d) 23/6
Answer : B

Question. The area (in sq. units) of the region A = {(x, y) ∈ R × R|0 d” x d”3, 0 d” y d” 4, y d” x2 + 3x} is :
(a) 53/6
(b) 8
(c) 59/6
(d) 26/3
Answer : C

Question. The area (in sq. units) of the region {(x, y) ∈R2|4x2 ≤ y ≤ 8x + 12} is: 
(a) 125/3
(b) 128/3
(c) 124/3
(d) 127/3
Answer : B

Question. If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then 02 xf'(x)dx is 
(a) 3/2
(b) 1
(c) 5/4
(d) –3/4
Answer : D

Question. The area (in sq. units) of the region A = {(x, y) : |x| + |y| ≤ 1, 2y2 ≥ |x|} is :
(a) 1/3
(b) 7/6
(c) 1/6
(d) 5/6
Answer : D

Question. For a > 0, let the curves C1: y2 = ax and C2: x= ay intersect at origin O and a point P. Let the line x = b (0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of ΔOQR = 1/2, then ‘a’ satisfies the equation: 
(a) x6 – 6x3 + 4 = 0
(b) x6 – 12x3 + 4 = 0
(c) x6 + 6x3 – 4 = 0
(d) x6 – 12x3 – 4 = 0
Answer : B

Question. The area (in sq. units) of the region A = {(x, y) : x2 ≤ y ≤ x + 2} is:
(a) 10/3
(b) 9/2
(c) 31/6
(d) 13/6
Answer : B

Question. The area (in sq. units) of the region enclosed by the curves y = x2 – 1 and y = 1 – x2 is equal to:
(a) 4/3
(b) 8/3
(c) 7/2
(d) 16/3
Answer : B

Question. The area of the region A = {(x, y): 0 ≤ y ≤ x |x| + 1 and – 1 ≤ x ≤ 1} in sq. units is:
(a) 2/3
(b) 2
(c) 4/3
(d) 1/3
Answer : B

Question. If the area (in sq. units) of the region {(x, y) : y2 ≤ 4x, x + y ≤ 1, x ≥ 0, y ≥ 0} is a √2 + b, then a – b is equal to :
(a) 10/3
(b) 6
(c) 8/3
(d) 2/3-
Answer : B

Question. The area enclosed between the curve y = loge (x + e) and the coordinate axes is
(a) 1
(b) 2
(c) 3
(d) 4
Answer : A

Question. The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = x and the straight line y = x, is:
(a) (24π – 1)
(b) (6π – 1)
(c) (12π – 1)
(d) (12π – 1)/6
Answer : D

Question. The region represented by |x - y| ≤ 2 and |x + y| ≤ 2 is bounded by a : 
(a) square of side length 2√2 units
(b) rhombus of side length 2 units
(c) square of area 16 sq. units
(d) rhombus of area 8√2sq. units
Answer : A

Question. Let 2 g(x) = cosx2 , f (x) = √x , and a, β (a < β) be the roots of the quadratic equation 18x2 - 9πx + π2 = 0 . Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = a,x = β and y = 0 , is :
(a) 1/2 (√3 + 1)
(b) 1/2 (√3 - √2)
(c) 1/2  (√2 - 1)
(d) 1/2 (√3 - 1)
Answer : D

Question. Consider a region R ={(x, y)∈R : x2 ≤ y ≤ 2x}. If a line y = a divides the area of region R into two equal parts, then which of the following is true?
(a) 3 2 a - 6a +16 = 0
(b) 2 3/ 2 3a -8a + 8 = 0
(c) 23a -8a + 8 = 0
(d) 3 3/ 2 a - 6a -16 = 0
Answer : B

Question. The area (in sq. units) of the region A = {(x , y): y2/2 ≤ x ≤ y + 4} is:
(a) 53/3
(b) 30
(c) 16
(d) 18
Answer : D

Question. If the area (in sq. units) bounded by the parabola y2 = 4λx and the line y = λx, λ > 0, is 1/9 , then λ is equal to :
(a) 2√6
(b) 48
(c) 24
(d) 4√3
Answer : C

Question. The area (in sq. units) of the region {(x, y) ∈ R2: x2 ≤ y ≤ |3 – 2x|, is:
(a) 32/3
(b) 34/3
(c) 29/3
(d) 31/3
Answer : A

Question. The area (in sq. units) of the region bounded by the curves y = 2x and y = |x + 1|, in the first quadrant is :
(a) log, 2 +3/2
(b) 3/2
(c) 1/2
(d) 3/2 - 1/log, 2
Answer : D

Question. Let S(a) = {(x, y) : y2 ≤ x, 0 ≤ x ≤ a} and A(a) is area of the region S(a). If for a λ, 0 < λ < 4, A(λ) : A(a) = 2 : 5, then λ equals :
(a) 2(4/25)1/3
(b) 2(2/5)1/3
(c) 4(2/5)1/3
(d) 4(4/25)1/3
Answer : D

Class_12_Mathematics_Worksheet_36 

 

1) Find the area enclosed by the parabola 𝑦 = 3𝑥2/4 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 3𝑥 − 2𝑦 + 12 = 0.

2) Find the area of the smaller region between the ellipse 9𝑥2 + 𝑦2 = 36 and the line 𝑥2 + 𝑦6 =1

3) Using integration find the area of region bounded by the triangle whose vertices are (1,0), (2,2) and (3,1).

4) Using the method of integration find the area region bounded by the lines x + 2y = 2,y-x = 1 and 2x + y = 7.

5) Find the area of the region enclosed between the two circles 𝑥2 +  𝑦2 =4 𝑎𝑛𝑑 (𝑥−2)2+𝑦2 = 4

6) Find the area of the region bounded by {(𝑥,𝑦):𝑥2 ≤ 𝑦 ≤ |𝑥|}

7) Find the area of the region bounded the curve y = √1−𝑥2, line y = x and the positive x- axis.

8) Using integration ,find the area of the following region: 
{(x,y):|𝑥−1|≤𝑦≤√5−𝑥2}

9) Find the area of the region bounded the curve y =4x - x2 and the x -axis.

10) Find the area of the region {(𝑥,𝑦):0≤𝑦≤𝑥2 +1,0≤𝑦 ≤ 𝑥+1,0 ≤ 𝑥 ≤ 2}

11) Find the area of the region {(𝑥,𝑦):𝑥2+𝑦2 ≤8𝑥,𝑦2 ≥ 4𝑥;𝑥 ≥ 0;𝑦≥0}

12) Find the area bounded by the curve y = 2x-x2 and the line y = -x .

13) Find the area bounded by the curves y = 6x – x2 and y = x2 – 2x.

14) Find the area bounded by the line x = 0, x = 2 and the curves y = 2x , y = 2x – x2.

1. Find the area bounded by the curve; y = √4-x , x-axis and y-axis.

2. Find the area bounded by the curves; y = x2 and x2 + y2 = 2 above x-axis.

3. Find the area bounded by; y = x2 – 4 and x + y = 2.

4. Find the area bounded by the circle; x2 + y2 = a2.

5. Find the area bounded by the curves; x2 + y2 = 4a2 & y2 = 3ax.

6. Find the area bounded by hyperbola x2 - y2 = a2 and the line x = 2a.

7. Find the area bounded by parabola y = x2, x-axis and the tangent to the parabola at (1,1).

8. Find the area of the portion of the circle x2 + y2 = 64 which is exterior to the parabola y2 = 12x. 

Q9. Draw the rough sketch of the curve y = I x + 1 I and evaluate the area bounded by the curve and the x – axis between x = -4 and x = 2.

Q10. Using integration find the area of the triangular region with vertices (1, 0), (2, 2) and (3,1).

Q11. Calculate the area of the region enclosed between the circles x2 + y2 = 16 and (2 + 4)2 + y=16

Q12. Find the area of the region bounded by the curve y = x2 + 2 and the lines y = x, x = 0, and x=3.

Q13. Find the area of the region {(x, y): x + y < 1 < x + y}

Q14. Using integration, find the area of the region :- {(x, y) : y2 < 4x, 4x2 + 4y2 < 9 }

Q15. Using integration, find the area of the region enclosed between the circles x2 + y2 = 4 and (x – 2)2 + y2 = 4

Q1. Find the area bounded by the curve y = √4x , x – axis and y – axis

Q2. Find the area bounded by the curves y = x2 and x2 + y2 = 2 above x – axis.

Q3. Find the area bounded by y = x2 – 4 and x = y = 2.

Q4. Find the area bounded by the circle x2 + y2 = a2

Q5. Find the area bounded by the curves :- x2 + y2 = 4a2 and y2 = 3ax

Q6. Find the area bounded by hyperbola x2 – y2 = a2 and the line x = 2a.

Q7. Find the area bounded by the parabola y = x2, x – axis and the tangent to the parabola at (1, 1).

Q8. Find the area of the protein of the circle x2 + y2 = 64 which is exterior to the parabola y2 = 12x.

Q9. Draw the rough sketch of the curve y = I x + 1 I and evaluate the area bounded by the curve and the x – axis between x = -4 and x = 2. 

Q10. Using integration find the area of the triangular region with vertices (1, 0), (2, 2) and (3,1).

Q11. Calculate the area of the region enclosed between the circles x2 + y2 = 16 and (2 + 4)2 + y2 = 16

Q12. Find the area of the region bounded by the curve y = x2 + 2 and the lines y = x, x = 0, and x=3.

Q13. Find the area of the region {(x, y): x + y < 1 < x + y}

Q14. Using integration, find the area of the region :- {(x, y) : y2 < 4x, 4x2 + 4y2 < 9 }

Q15. Using integration, find the area of the region enclosed between the circles x2 + y2 = 4 and (x – 2)2 + y2 = 4

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CBSE Class 12 Mathematics Chapter 8 Application Of Integrals Worksheet

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Worksheet for Mathematics CBSE Class 12 Chapter 8 Application Of Integrals

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Chapter 8 Application Of Integrals worksheet Mathematics CBSE Class 12

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Chapter 8 Application Of Integrals CBSE Class 12 Mathematics Worksheet

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Worksheet for CBSE Mathematics Class 12 Chapter 8 Application Of Integrals

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