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Show that: int0^(pi//2)f(sin2x)sinxdx...

Show that: `int_0^(pi//2)f(sin2x)sinxdx=sqrt(2)int_0^(pi//4)f(cos2x)cosxdxdot`

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If the function f : [-1,1] to R is continuous and even, then show that int_(0)^(pi//2)f(cos2x)cosxdx=sqrt(2)int_(0)^(pi//4)f(sin2x)cosxdx .

int_0^(pi/2) sqrt(cosx)sinxdx

Evaluate : int_0^(pi/2)x^2sinxdx

If I_1=int_0^(pi/2)f(sinx)sinxdx and I_2=int_0^(pi/2)f(cosx)cosxdx then I_1/I_2

Prove that : int_0^(pi/2)sqrt(1-sin2x)dx=2(sqrt(2)-1)

Show that (i) int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x (ii) int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x (iii) int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x

Evaluate: int_0^(pi//4)sqrt(1+sin2x)dx (ii) int_0^(pi//4)sqrt(1-sin2x)dx

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

Evaluate : int_0^(pi/2)(sin^2x)/(sin x+cos x)dx

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Find the equation of tangent to the y = F(x) at x = 1, where F(x) = u...

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  2. If int0^x[x]dx=int0^([x])xdx , then prove that either x is purely fr...

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  3. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

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  4. IfI1=int0^1 2^(x^2)dx ,I2=int0^1 2^(x^3)dx ,I3=int1^2 2^(x^2)dx ,I4=in...

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  5. If af(x)+bf((1)/(x))=(1)/(x)-5,x ne 0,a ne b, then overset(2)underset(...

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  6. Find the mistake in the following evaluation of the integral I=int0^pi...

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  7. Find the value of int(-1)^1d/(dx)(tan^(-1)(1/x))dx

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  8. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dx is

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  9. The value of int(-2)^2|1-x^2|dx is

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  10. If II=int0^(pi//2)cos(sinx)dx ,I2=int0^(pi/2)sin(cosx)dx \ ,a n d \ I3...

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  11. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  12. Evaluate the following limit: lim(nto oo)(sum(r=1)^(n) sqrt(r)sum(r=...

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  13. Evaluate: ("lim")(n rarr oo)[(n !)/(n^n)]^(1//n)

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  14. If the value of the definite integral int0^1 "^(207)C7x^(200)(1-x)^7dx...

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  15. Evaluate: int(-1)^0(dx)/(x^2+2x+2)

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  16. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a ...

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  17. If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int(-1)^1...

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  18. Evaluate: int0^pie^(|cosx|)(2sin(1/2cosx)+3cos(1/2cosx))sinxdxdot

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  19. Evaluate: inta^b x^3dx

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  20. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

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