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The number of positive continuous f(x) d...

The number of positive continuous `f(x)` defined in `[0,1]` for with `I_(1)=int_(0)^(1)f(x)dx=1,I_(2)=int_(0)^(1)xf(x)dx=a`,
`I_(3)=int_(0)^(1)x^(2)f(x)dx=a^(2)` is /are

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The numbers of possible continuous f(x) defined in [0,1] for which I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx-a ,I_3=int_0^1x^2f(x)dx=a^2i s//a r e 1 (b) oo (c) 2 (d) 0

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

Let I_(1)=int_(0)^(pi//4)e^(x^(2))dx, I_(2) = int_(0)^(pi//4) e^(x)dx, I_(3) = int_(0)^(pi//4)e^(x^(2)).cos x dx , then :

If I_(1)=int_(0)^(2pi)sin^(3)xdx and I_(2)=int_(0)^(1)ln((1)/(x)-1)dx , then

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =

If I_(1)=int_(0)^(pi//2) cos(sin x) dx,I_(2)=int_(0)^(pi//2) sin (cos x) dx and I_(3)=int_(0)^(pi//2) cos x dx then

If I_(1)=int_(0)^(1) 2^(x^(2)) dx, I_(2)=int_(0)^(1) 2^(x^(3)) dx, I_(3)=int_(1)^(2) 2^(x^(2))dx and I_(4)=int_(1)^(2) 2^(x^(3))dx then

Let I_(1)=int_(0)^(1)(|lnx|)/(x^(2)+4x+1)dx and I_(2)=int_(1)^(oo)(lnx)/(x^(2)+4x+1)dx , then

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

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

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

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

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

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

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

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

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

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  10. Evaluate: int0^pixlogsinxdx

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

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

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  13. T h ev a l u eofint1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dxi...

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

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

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  16. Find the value of : int0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denote...

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  17. The range of the function f(x)=int(-1)^1(sinxdt)/((1-2tcosx+t^2) is

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

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  19. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0)=0,x in R , w...

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

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