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If f(a+b-x)=f(x)," then "int(a)^(b)xf(x)...

If `f(a+b-x)=f(x)," then "int_(a)^(b)xf(x)dx=`

A

`(a+b)/(2)int_(a)^(b)f(x)dx=`

B

`(a-b)/(2)int_(a)^(b)f(x)dx=`

C

`(a-b)/(2)int_(a)^(b)f(a+b-x)dx`

D

`(a+b)/(2)int_(a)^(b)f(b-x)dx`

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DIPTI PUBLICATION ( AP EAMET)-DEFINITE INTEGRATION-EXERCISE 1B
  1. If f(x) is intergrable on [0,a] then int(0)^(a)(f(x))/(f(x)+f(a-x))dx=

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  2. int(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=

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  3. If f(a+b-x)=f(x)," then "int(a)^(b)xf(x)dx=

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  4. int(2)^(3)(sqrtx)/(sqrt(5-x)+sqrtx)dx

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  5. The value of the integral, int(3)^(6)(sqrtx)/(sqrt(9-x)+sqrtx)dx is

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  6. int(-a)^(b)(root(3)(x+a))/(root(3)(x+a)+root(3)(b-x))dx=

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  7. If f(x)=(e^(x))/(1+e^(x)),I(1)=int(f(-a))^(f(a))xg{x(1-x)}dxandI(2)=in...

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  8. Let l=int(0)^(1)(sinx)/(sqrtx)dxandI=int(0)^(1)(cosx)/(sqrtx)dx. Then ...

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  9. int(pi//8)^(3pi//8)(1)/(1+cotx)dx=

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  10. int(-2)^(2)(x^(11)cosx+e^(x))dx=

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  11. int(-1)^(1)log((2+x)/(2-x))dx=

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  12. int(-pi//2)^(pi//2)log((2-sintheta)/(2+sintheta))d""theta=

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  13. int(-pi//4)^(pi//4)((x+pi//4)/(2-cos2x))dx=

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  14. int(-1)^(+1)(d)/(dx)(Tan^(-1)1//x)dx=

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  15. The value of int(-pi//2)^(pi//2)(x^(3)+xcosx+tan^(5)x+1)dx=

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  16. int(-3pi//2)^(-pi//2)[(x+pi)^(3)+cos^(2)(x+3pi)]dx=

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  17. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1andg(x) be a f...

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  18. If f''(x)andf'(x) are continuous on [a,b] then int(a)^(b)xf''(x)dx=

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  19. If f(x) and g(x) are continuous functions satisfysing f(x)=f(a-x)andg(...

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  20. int(-1)^(1)(sqrt(1+x+x^(2))-sqrt(1-x+x^(2)))/(sqrt(1+x+x^(2))+sqrt(1-x...

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