#### Important 5 mark questions- 1

11th Standard

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Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 75

Part A

15 x 5 = 75
1. Integrate the following with respect to x: ex

2. Integrate the following with respect to x:$(1+x^2)^{-1}$

3. Integrate the following with respect to x:$(1+x^2)^{-{1\over 2}}$

4. Integrate the following functions with respect to x:$sec^2{x\over5}$

5. Integrate the following functions with respect to x: cosec(5x+3)cot(5x+3)

6. Integrate the following functions with respect to x: 30sec(2-15x)tan(2-15x)

7. Integrate the following functions with respect to x:${1\over \sqrt{1-(4x)^2}}$

8. Integrate the following functions with respect to x:${1\over \sqrt{1-81x^2}}$

9. Integrate the following functions with respect to x:${1\over 1+36x^2}$

10. Integrate the following with respect to x:${6\over 1+(3x+2)^2}-{12\over \sqrt{1-(3-4x)^2}}$

11. A wound is healing in such a way that t days since Sunday the area of the wound has been decreasing at a rate of $-{3\over(t+2)^2}cm^2$ per day. If on Monday the area of the wound was 2 cm2
(i) What was the area of the wound on Sunday?
(ii) What is the anticipated area of the wound on Thursday if it continues to heal at the same rate?

12. Integrate the following with respect to  x(1-x)17

13. Evaluate : $\int tan^{-1}({2x\over 1-x^2})dx$

14. Integrate the following with respect to x:${log \ x \over (1+log x)^2}$

15. Integrate the following functions with respect to x :$\sqrt{(x+1)^2-4}$