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Evaluate : (i) underset(0)overset(1)in...

Evaluate :
(i) `underset(0)overset(1)intsin^(-1)xdx` , (ii) `underset(1)overset(2)int(lnx)/(x^(2))dx`, (iii) `underset(0)overset(1)intx^(2)sin^(-1)xdx`.

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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Self practive problem
  1. Evaluate : (i) int(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int(sqrt(2))^(...

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  2. Evaluate : (i) int(0)^(1)sin^(-1)xdx , (ii) int(1)^(2)(lnx)/(x^(2))d...

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  3. Evaluate : (i) underset(0)overset(1)intsin^(-1)xdx , (ii) underset(1...

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  4. Integrate 1/(1+x2) for limit [0,1].

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  5. Evaluate : int( (dx)/(e^(x)+e^(-x)) )

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  6. Let f(x) = ln ((1-sinx)/(1+sinx)), then show that int(a)^(b) f(x)dx =...

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  7. Evaluate : int(0)^(pi)sqrt(1+sin2x)dx .

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  8. Evaluate : int(-1)^(1)e^(x)dx

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  9. Evaluate : int(0)^(pi) (dx)/(5+4cosx)

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  10. Evaluate : int(0)^(pi) (dx)/(5+4cosx) . a) π b) π/2 c) π/3 d) π/4

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  11. Evaluate : (i) int(-1)^(2){2x}dx (where function{*} denotes fraction...

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  12. It is known that f(x) is an odd function and has a period p. Prove tha...

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  13. (i) If f(x) = int(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int(0)^(cos^(2)x)cos^...

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  14. If y = int(1)^(x) xsqrt(lnt)dt then find the value of (d^(2)y)/(dx^(...

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  15. lim(n to oo)(int(1//(n+1))^(1//n)tan^(-1)(nx)dt)/(int(1//(n+1))^(1//n)...

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  16. Let f be a differentiable function on R and satisfying the integral eq...

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  17. Evaluate : int(0)^(2)x^(3//2)sqrt(2-x)dx.

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  18. Prove the following inequalities : (i) (sqrt(3))/(8) lt int(pi//4)^(...

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  19. Show that (i) (1)/(10sqrt(2))lt underset(0)overset(1)int(x^(9))/(sq...

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  20. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n+1)dot

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