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Evaluate the following integral: int(-pi...

Evaluate the following integral: `int_(-pi)^pix^(10)sin^7x\ dx`

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`int_{-pi}^{pi} x^{10} sin ^{7} x d x`

` Let f(x)=x^{10} sin ^{7} x`

Consider `f(-x)=(-x)^{10} sin ^{7}(-x)=-x^{10} sin ^{7} x=-f(x)`

Hence `f(x)` is an odd function

Therefore

`int_{-pi}^{pi} x^{10} sin ^{7} x d x=0`

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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int0^pix/(1+cosalphas in x)dx

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  2. Evaluate the following integral: int0^(pi//2)x/(sinx+cos x)dx

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  3. Evaluate the following integral: int(-pi)^pix^(10)sin^7x\ dx

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  4. Evaluate the following integral: int0^pi(dx)/(6-cosx)

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  5. Evaluate the following integral: int0^(pi//4)tan^4x\ dx

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  6. Evaluate the following integral: int1^3|x^2-2x|dx

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  7. Evaluate the following integral: int0^pi |sin^2x|dx

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  8. Evaluate the following integral: int(-pi//2)^(pi//2)sin^9x\ dx

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  9. Evaluate the following integrals: int0^pi(x/(1+sin^2x)+cos^7x)dx

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  10. Evaluate the following integral: int0^(pi//2)1/(1+tan^3x)dx

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  11. Evaluate the following integral: int0^pixsinxcos^4x\ dx

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  12. Evaluate the following integral: int(-pi//4)^(pi//4)|sinx|dx

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  13. Evaluate the following integral: int0^pix/(1+cos alpha sin x)dx

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  14. Evaluate the following integral: int0^(pi//2)x/(sinx+cos x)dx

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  15. Evaluate int0^pi x/(a^2-cos^2x)dx

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  16. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s

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  17. Evaluate the following integral: int0^(pi//2)xsinx+cos^2x

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  18. int0^1cot^(- 1)(1-x+x^2)dx

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  19. Evaluate the following integral: int0^(pi//2)1/(2cos x+4sinx)dx

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  20. Evaluate the following integral: int(pi//6)^(pi//2)(cos e c\ xcotx)/(1...

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