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# Application of Integrals Test-5 Class 12 Notes | EduRev

## Class 12 : Application of Integrals Test-5 Class 12 Notes | EduRev

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CBSE TEST PAPER-05
CLASS - XII MATHEMATICS (Calculus : Application of Integrals)
Topic: - Application of Integrals
Note : Each Question carries 6 marks.
1. Find the area of the smaller region bounded by the ellipse
2 2
2 2
1
x y
a b
+ = and the line
1.
x y
a b
+ =
2. Find the area of the region enclosed by the parabola x
2
= y, the line y = x +2 and the
x – axis.
3. Using method of integration, find the area bounded by the curve |x| + |y| = 1.
4. Find area bounded by curves ( ) { }
2
, : and | | . x y y x y x = =
5. Using method of integration find the area of the triangle ABC, coordinates of whose
vertices are A (2, 0), B (4, 5) and C (6, 3).
6. Using method of integration, find the area of the region bounded by lines:
2x + y = 4, 3x – 2y = 6
and x – 3y + 5 = 0.
7. Find the area of two regions ( ) { }
2 2
, : 4 ,4 2 4 9 . x y y x x y = + =
8. Find the area of the circle x
2
= y
2
= 15 exterior to the parabola y
2
= 6x
9. Find the area bounded by the y – axis, y = cosx and y = sinx, 0
2
x
p
= =
10. Using integration, find the area of the region in the first quadrant enclosed by the
x – axis, the line y = x and the circle x
2
+ y
2
= 32.
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