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Evaluate: int(-pi)^pi(1-x^2)sinxcos^2xdx...

Evaluate: `int_(-pi)^pi(1-x^2)sinxcos^2xdx`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

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  2. The value of int0^(pi/2)dx/(1+tan^3x) is

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  3. Evaluate: int(-pi)^pi(1-x^2)sinxcos^2xdx

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  4. Let f be a contiuous function on [a,b]. If F(x)=(int(a)^(x)f(t)dt-int(...

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  5. Evaluate the following: int(-1)^(1)(sin x-x^(2))/(3-|x|)dx

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  6. If int(a)^(b)|sinx|dx=8 and int(0)^(a+b)|cosx|dx=9, then find the valu...

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  7. Evaluate: int(-pi/2)^(pi/2)sqrt(cos^(2n-1)x-cos^(2n+1)x)dx ,w h e r en...

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  8. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

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  9. Evaluate: int(-1/2)^(1/2)cosxlog((1-x)/(1+x))dx

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  10. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

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  11. Evaluate: int0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[do...

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  12. Suppose f is a real-valued differentiable function defined on [1,oo] ...

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  13. Let f be a real valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) ...

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  14. If x int(0)^(x)sin(f(t))dx=(x+2)int(0)^(1)tsin(f(t))dt, where xgt0, th...

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  15. Evaluate: int0^2(dx)/((17+8x-4x^2)[e^(6(1-x))+1]

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  16. I f f(x)=int((pi^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta...

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  17. Find the equation of tangent to the y = F(x) at x = 1, where F(x) = u...

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  18. If int0^x[x]dx=int0^([x])xdx , then prove that either x is purely fr...

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  19. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

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  20. If I1=int0^1 2^(x^2)dx , I2=int0^1 2^(x^3) dx , I3= int1^2 2^(x^2) dx ...

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