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Evaluate the following: int0^(pi//4) (si...

Evaluate the following: `int_0^(pi//4) (sin^2 x \ cos^2 x)/(sin^3x + cos^3 x)^2 \ dx`

A

`(1)/(6)`

B

`(1)/(12)`

C

`(1)/(4)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
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MARVEL PUBLICATION-INTEGRATION - DEFINITE INTEGRALS -MULTIPLE CHOICE QUESTIONS (PART - B : Mastering The BEST)
  1. Find the value of int0^1x(1-x)^ndx

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  2. If inta^b x^3dx=0,a n d"I f"inta^b x^2dx=2/3,"f i n dr e a lv a l u...

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  3. Evaluate the following: int0^(pi//4) (sin^2 x \ cos^2 x)/(sin^3x + cos...

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  4. If f(x)=f(4-x), g(x)+g(4-x)=3 and int(0)^(4)f(x)dx=2, then : int(0)^(4...

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  5. If f(a-x)=f(x) and int(0)^(a//2)f(x)dx=p, then : int(0)^(a)f(x)dx=

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  6. Evaluate: int(-1/2)^(1/2)cosxlog(1-x)/(1+x)dx

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  7. int(-pi)^(pi)(1-x^(2))sin x cos^(2)x dx=

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  8. If {:(f(x)=x", ...."x lt 1),(" "=x-1", ...." x ge 1","):} ...

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  9. If 0 le alpha le 2pi and int(0)^(alpha)cos x dx = cos 2alpha, the : al...

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  10. int(-2)^(3)[cot^(-1)((x-1)/(x+1))+cot^(-1)((x+1)/(x-1))]dx=

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  11. If f(x)+f(pi-x)=1 and g(x)+g(pi-x)=1, then : int(0)^(pi)[f(x)+g(x)]dx=

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  12. int(0)^(pi//2)(1)/(sqrt(tan x)-sqrt(cot x))dx=

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  13. If int(-3)^(2)f(x)dx=2 and int(2)^(5)[5+f(x)]dx=9, then : int(5)^(-3)f...

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  14. If (d)/(dx)[g(x)]=f(x), then : int(a)^(b)f(x)g(x)dx=

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  15. If int(0)^(1)f(x)dx=1, int(0)^(1)x f(x)dx=a and int(0)^(1)x^(2)f(x)dx=...

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  16. If int(0)^(a)(1)/(1+4x^(2))dx=(pi)/(8), then a =

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  17. int(0)^(pi//2)((pi)/(4)-x)/(sqrt(sin x)+ sqrt(cos x))dx=

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  18. int(-pi//2)^(pi//2)sin (|x|)dx=

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  19. int(-pi//2)^(pi//2)(1)/(1+e^(sin x))dx=

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  20. The value of the definite integral int0^1(1/(x^2+2xcosalpha+1))dx for ...

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