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If int0^a3x^2dx=8,\ write the value of ...

If `int_0^a3x^2dx=8,\ ` write the value of `' a^(prime)dot`

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`int_0^a3x^2dx=8`
`Rightarrow [(3x^3)/3]_0^alpha = 8`
`Rightarrow [x^3]_0^alpha = 8`
`Rightarrow (alpha)^3 = 8`
`therefore alpha = 2`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate each of the following integral: int2^4x/(x^2+1)dx

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  2. If int0^1(3x^2+2x+k)dx=0, find the value of kdot

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  3. If int0^a3x^2dx=8,\ write the value of ' a^(prime)dot

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  4. If (x)=int0^x tsint\ dt ,\ then write the value of f^(prime)(x)

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  5. If int0^a1/(4+x^2)dx=pi/8 , find the value of adot

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  6. The value of int-2^2 (ax^3+bx+c)dx depends on (A) the value of b (B) t...

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  7. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  8. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  9. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  10. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  11. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  12. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  13. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  14. If [dot]a n d\ {dot} denote respectively the greatest integer and frac...

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  15. The value of int0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(s in x))dx is ...

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  16. int0^(pi/2) 1/(1+sinx)dx equals 0 b. 1//2 c. 2 d. 3//2

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  17. int0^oo1/(1+e^x)dx equals a. log2-1 b. log2 c. log4-1 d. log2

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  18. The value of int0^(2pi)sqrt(1+sin (x/2)dx is 0 b. 4 c. 2 d. 8

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  19. int0^(pi^2//4)(sinsqrt(x))/(sqrt(x))dx equals a. pi^2//8 b. pi//4 ...

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  20. int0^(pi//2)1/(2+cos\ x)dx equals 1/3tan^(-1)(1/(sqrt(3))) b. 2/(sqrt(...

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