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Evaluate: int(-pi/4)^(pi/4)(x^9-3x^5+7x^...

Evaluate: `int_(-pi/4)^(pi/4)(x^9-3x^5+7x^3-x+1)/(cos^2x)dx`

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Verified by Experts

`f(x)=(x^(9)-3x^(5)+7x^(3)-x)/(cos^(2)x+sec^(2)x)`
`sec^(2)x(x^(9)-3x^(5)+7x^(3)-x)+sec^(2)x`
`:.int_(pi//4)^(pi//4)f(x)dx=int_(-pi//4)^(pi//4)sec^(2) xdx`
`[ :' sec^(2)x(x^(9)-3x^(5)+7x^(3)-x)` is an odd function]
`=2int_(0)^(pi//4)sec^(2) xdx`
`=2[tanx]_(0)^(pi//4)=2`
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CENGAGE ENGLISH-DEFINITE INTEGRATION -JEE ADVANCED
  1. Evaluate: int(-pi/4)^(pi/4)(x^9-3x^5+7x^3-x+1)/(cos^2x)dx

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  2. Let f be a non-negative function defined on the interval [0,1]. If int...

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  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

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  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  5. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

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  6. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)for...

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  7. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  8. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

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  10. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

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  11. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

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  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

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  13. about to only mathematics

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  14. Let S be the area of the region enclosed by y=e^-(x^2),y=0,x=0,a n dx=...

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  15. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

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  16. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

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  17. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^(t+(1)...

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  18. The option(s) with the values of aa n dL that satisfy the following eq...

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  19. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

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  20. find the period of sin(x/2)-cos(x/3) is

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  21. Let f: Rvec(0,1) be a continuous function. Then, which of the followin...

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