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Show that int0^(pi/2)sqrt((sin2theta))si...

Show that `int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4`

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int_(0)^(pi)(sin4theta)/(sintheta)d theta=0

int_(0)^((pi)/(2))cos^(4)thetad theta

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Evaluate: int_(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a >0

If r=2(1-costheta) , then show that, int_(0)^(pi)sqrt(r^(2)+((dr)/(d theta))^(2))d theta=8

If int_0^(pi/2) sintheta log sintheta d theta =log (A/(198e) then the last digit of A is equal to

int_(0)^((pi)/(4))thetasec^(2)thetad theta

If int_0^(pi/2)logsinthetad(theta)=k , then find the value of int_0^(pi/2)(theta/(sintheta))^2d(theta) in terms of k

if I=int_0^(pi/4) (sin2theta)/(sin^2theta+cos^4theta)d(theta) then I equals

If I_1=int_0^(pi/2)costhetaf(sintheta+cos^2theta)d(theta) and I_2=int_0^(pi//2)sin2thetaf(sintheta+cos^2theta)d(theta) , then (a) I_1=-2I_2 (b) I_1=I_2 (c) 2I_1=I_2 (d) I_1=-I_2

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: int(-pi)^pi(xsinx dx)/(e^x+1)

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  2. Ifint0^1cot^(-1)(1-x+x^2)dx=lambdaint0^1tan^(-1)x dx ,then lambda is e...

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  3. Show that int0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

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  4. The number of positive continuous f(x) defined in [0,1] for with I(1)=...

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  5. int 0^(pi/2) (sin^2x)/(sinx+cosx)dx

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  6. The value of the definite integral int0^(pi/2)sqrt(tanx)dx is (a) s...

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  7. For theta in (0,pi/2), prove that int0^theta"log"(1+tanthetatanx)dx=th...

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  8. A function f is defined by f(x)=1/(2^(r-1)),1/(2^r)ltxlt=1 (2^(r-1)),...

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  9. Evaluate int0^1(dx)/((5+2x-2x^2)(1+e^(2-4x))) dx

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  10. If P(x) is a polynomial of the least degree that has a maximum equal t...

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  11. Evaluate: int0^pixlogsinxdx

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  12. The value of the definite integral int0^(sqrt(1n(pi/2)))cose^(x^(2)...

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  13. Evaluate: int0^(π/2)cos2x+4sin2x cos2xdx

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  14. The value of int1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dx is...

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  15. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

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  16. If f(x) is monotonic differentiable function on [a , b] , then int...

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  17. L e tA=int0^oo(logx)/(1+x^3)dx Then find the value of int0^oo(xlogx)/(...

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  18. Show that : int0^1(logx)/((1+x))dx=-int0^1(log(1+x))/x dx

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  19. The value of lim(n->oo) [tan(pi/(2n)) tan((2pi)/(2n))........tan((npi...

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  20. answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...

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