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int(0)^((pi)/(2)) sin^7 xdx is :...

`int_(0)^((pi)/(2)) sin^7 xdx` is :

A

`pi//2`

B

`pi//4`

C

`pi//6`

D

`3pi//2`

Text Solution

Verified by Experts

The correct Answer is:
B
`sin^(3)x=3/4 sinxx =1/4 sinx 3x`
`:. int_(0)^(oo) (sin^(3)x)/x dx=3/4 int_(0)^(oo) (sinx)/x dx-1/4 int_(0)^(oo) (sin 3x)/x dx`
`=3/4 int_(0)^(oo) (sinx)/x dx-1/4 int_(o)^(oo) (sinu)/u du (u=3x)`
`=3/4 (pi)/2-1/4 (pi)/2=(pi)/4`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
  1. Evaluate the definite integrals int(0)^((pi)/(4))(sinx+cosx)/(9+16s...

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  2. int(1)^(2)x^(2)dx is equal to

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  3. int(0)^((pi)/(2)) sin^7 xdx is :

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  4. The range of the function f(x)=int(-1)^1(sinxdt)/((1-2tcosx+t^2)i s [...

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  5. If the function f:[0,8]vecR is differentiable, then for 0<a , b<2,int0...

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  6. If f(x)=xtan^(-1)x, then f'(1) is

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  7. Let f(0)=0a n dint0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)...

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  8. If f(x)="cos"(tan^(-1)x), then the value of the integral int0^1xf^(x)d...

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  9. The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)...

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  10. The value of int1^e((tan^(-1)x)/x+(logx)/(1+x^2))dxi s tane (b) tan^...

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  11. Iff(pi)=2int0^pi(f(x)+f^(x))sinxdx=5,t h e nf(0) is equal to (it is g...

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  12. If int1^2e^x^2dx=a ,t h e ninte^(e^4)sqrt(1n x)dxi se q u a lto 2e^4-...

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  13. If f(x) is continuous for all real values of x , then sum(r=1)^nf(r-1...

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  14. T h ev a l u eofint0^(pi/2)sin|2x-alpha|dx ,w h e r ealpha in [0,pi],i...

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  15. f(x) is a continuous function for all real values of x and satisfies i...

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  16. If f(x) = int(0)^(x) t cos t dt, then (df)/(dx)

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  17. If agt0 and A=int(0)^(a)cos^(-1)xdx, and int(-a)^(a)(cos^(-1)x-sin^(...

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  18. The value of int1^a[x]f^(prime)(x)dxf^(prime)(x)dx ,w h e r ea >1,a n ...

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  19. int3^(10)[log[x]]dxi se q u a lto(w h e r e[dot]r e p r e s e t n tt h...

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  20. int(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer...

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