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The value of int0^1e^(x^2-x)dx is (a)<1 ...

The value of `int_0^1e^(x^2-x)dx` is (a)`<1` (b) `>1` (c) `> e^(-1/4)` (d) `none of these

A

`lt1`

B

`gt1`

C

`gte^(-1/4)`

D

`lte^(-1/4)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`int_(0)^(1)e^(x^(2)-x)dx`
For `x epsilon(0,1),x^(2)-x epsilon(-1//4,0)`
`:.e^(-1//4)lt e^(x^(2)-x)lte^(0)`
or `e^(-1/4)lt int_(0)^(1)e^(x^(2)-x)dxlt1`
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CENGAGE-DEFINITE INTEGRATION -Exercise (Multiple)
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  2. IfAn=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ,bn=int0^(pi/2)((sinn x)/(sinx))...

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  3. T h ev a l u eofint0^oo(dx)/(1+x^4)i s s a m ea st h a tofint0^oo(x^...

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

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  5. Ifinta^b(f(x))/(f(a)+f(a+b-x))dx=10 ,t h e n b=22 ,a=2 (b) b=15 ,1=-...

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  6. The values of a for which the integral int0^2|x-a|dxgeq1 is satisfied ...

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  7. If f(x)=int(0)^(x)|t-1|dt, where 0lexle2, then

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  8. Evaluate int(0)^(1)x(1-x)^3dx

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

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  10. If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then

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  11. IfIn=int0^1(dx)/((1+x^2)^n),w h e r en in N , which of the following...

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  12. L e tf:[1,oo)vecRa n df(x)=int1^x(e^t)/t dt-e^xdotT h e n f(x) is an ...

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  13. Iff(x)=inta^x[f(x)]^(-1)dxa n dinta^1[f(x)]^(-1)dx=sqrt(2),t h e n f(...

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  14. A continuous function f(x) satisfies the relation f(x)=e^x+int0^1 e^xf...

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  15. int0^x{int0^uf(t)dx}d ui se q u a lto int0^x(x-u)f(u)d u int0^x uf(...

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  16. Evaluate int(0)^(1) 6^x dx

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  17. Evaluate int(0)^(2)7^xdx

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  18. Evaluate int(0)^(1)x(1-x)dx

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  19. Check whether the given equation is a quadratic equation. i) (x+1)^2...

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  20. Let f(x) be a non-constant twice differentiable function defined on (o...

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