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#### Applications of Integration Five Marks Questions

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. Evaluate$\int _{ 0 }^{ 1 }{ x^3dx }$, as the limit of a sum.

2. Evaluate$\int _{ 1 }^{ 4 }{ ({ 2x }^{ 2 }-3) }$ dx, as the limit of a sum

3. Evaluate $\int _{ 0 }^{ x }{ { x }^{ 2 } }$cos nxdx, where n is a positive integer.

4. Evaluate: $\\ \\ \int _{ -1 }^{ 1 }{ { e }^{ -\lambda x }(1-{ x }^{ 2 }) } dx$

5. Evaluate $\int ^\frac {\pi}{2}_{0}$( sin2 x + cos4 x ) dx

6. Evaluate $\int _{ 0 }^{ 1 }{ { x }^{ 5 }{ (1-{ x }^{ 2 }) }^{ 5 }dx }$

7. Evaluate $\int _{ 0 }^{ 1 }{ { x }^{ 3 }{ (1-x) }^{ 4 }dx }$

8. Find the area of the region bounded between the parabola y2 ax = 4
and its latus rectum

9. Find the area of the region bounded between the parabolas y2 x = 4 and x2 y = 4.

10. Using integration find the area of the region bounded by triangle ABC, whose vertices A, B, and C are (−1,1), (3, 2), and (0,5) respectively