Ncert Solutions for Class 12
Integrals
Integrals
Exercise 7.1
Find an anti derivative (or integral) of the following functions by the method of inspection.
1. (int{sin{2}xdx})
2. (int{cos{3}xdx})
3. (int{e^{2x}dx})
4. (int{left(ax+bright)^2dx})
5. (int{sin{2}x-4e^{3x}dx})
Find the following integrals in Exercises 6 to 20:
6. (intleft(4e^{3x}+1right)dx)
7. (int{x^2left(1-frac{1}{x^2}right)dx})
8. (intleft(ax^2+bx+cright)dx)
9. (intleft(2x^2+e^xright)dx)
10. (int{left(sqrt x-frac{1}{sqrt x}right)^2dx})
11. (int{frac{x^3+5x^2-4}{x^2}dx})
12. (int{frac{x^3+3x+4}{sqrt x}dx})
13. (int{frac{x^3-x^2+x-1}{x-1}dx})
14. (int{left(1-xright)sqrt x dx})
15. (int{sqrt xleft(3x^2+2x+3right)dx})
16. (intleft(2x-3cos{x}+e^xright)dx)
17. (intleft(2x^2-3sin{x}+5sqrt xright)dx)
18. (int{sec{x}left(sec{x}+tan{x}right)dx})
19. (int{frac{{sec}^2{x}}{cos{e}c^2x}dx})
20. (int{frac{2-3sin{x}}{{cos}^2{x}}dx})
Choose the correct answer in Exercises 21 and 22.
21. The anti derivative of (left(sqrt x+frac{1}{sqrt x}right)) equals
(A) (frac{1}{3}x^frac{1}{3}+2x^frac{1}{2}+C)
(B) (frac{2}{3}x^frac{2}{3}+frac{1}{2}x^2+C)
(C) (frac{2}{3}x^frac{3}{2}+2x^frac{1}{2}+C)
(D) (frac{3}{2}x^frac{3}{2}+frac{1}{2}x^frac{1}{2}+C)
22. If (frac{d}{dx}fleft(xright)=4x^3-frac{3}{x^4}) such that (fleft(2right)=0). Then (fleft(xright)) is
(A) (x^4+frac{1}{x^3}-frac{129}{8})
(B) (x^3+frac{1}{x^4}+frac{129}{8})
(C) (x^4+frac{1}{x^3}+frac{129}{8})
(D) (x^3+frac{1}{x^4}-frac{129}{8})