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Let: f(x)=int0^x|2t-3|dtdot Then discuss...

Let: `f(x)=int_0^x|2t-3|dtdot` Then discuss continuity and differentiability of `f(x)at x=3/2`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Show that inta^b(|x|)/x dx=|b|-|a|dot

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  2. The value of (pi^2)/(1n3)int(7/6)^(5/6)sec(pix)dxi s

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  3. Let: f(x)=int0^x|2t-3|dtdot Then discuss continuity and differentiabil...

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  4. If inta^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is

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  5. L e tI1=int(pi/6)^(pi/3)(sinx)/x dx ,I2=int(pi/6)^(pi/3)sin(sinx)/(sin...

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  6. The value of int0^1e^(x^2-x)dx is (a)<1 (b) >1 (c) > e^(-1/4) ...

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  7. Evaluate: int0^(1)x(dx)/(sqrt(1-x^(2)))

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  8. The value of the definite integral int(0)^(1)(1+e^(-x^(2))) dx is

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  9. Prove that 0 lt int0^1(x^7dx)/((1+x^8)^(1/3)) lt 1/8

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  10. Let a , b , c be nonzero real numbers such that int0^1(1+cos^8x)(a x^2...

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  11. Evaluate: 5050(int0^1(1-x^(50))^(100)dx)/(int0^1(1-x^(50))^(101)dx)

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  12. Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^ycostdt=0,then evaluate (dy)/(d...

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  13. If f(x)=int0^x("cos"(sint)+"cos"(cost)dt ,t h e nf(x+pi)i s (a)f(x)+f...

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  14. Evaluate: int(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a ...

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  15. Evaluate: int(0)^1(dx)/(1+x^2)

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  16. If f(t) is an odd function, then prove that varphi(x)=inta^xf(t)dt is ...

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  17. Evaluate: int2^3(2x^5+x^4-2x^3+2x^2+1)/((x^2+1)(x^4-1))dx

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  18. Find the value of int(0)^(1){(sin^(-1)x)//x}dx.

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  19. Show that int0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive int...

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  20. Find I=int0^pi ln(1+cosx)dx

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