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

If `int_0^1(3x^2+2x+k)dx=0,` find the value of `kdot`

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Given,`int_0^1(3x^2+2x+k)dx=0,`
=`[x^3+x^2+kx]_0^1​=0`
=`(1+1+k)−0=0`
`k=−2`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
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  2. Evaluate: (i)int0^4 1/(sqrt(x^2+2x+3))dx

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

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  4. If int1^a (3x^2 + 2x +1)dx = 11 then the value of a is

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  5. If inta^b x^3dx=0, and If inta^b x^2dx=2/3, find a and b.

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  6. Evaluate: int0^(pi//2)sqrt(1-cos2x)dxdot

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  7. Evaluate: int0^(pi//2)sin^4xdx

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  9. Evaluate: int(pi//4)^(pi//2)sqrt(1-sin2x)dx

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  11. Evaluate the following integrals: (1-35) int0^pixsinx cos^2x dx

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  14. Evaluate the following integrals: (1-35) int0^(pi//2)(sin^n x)/(sin...

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  15. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx= pi^2

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  16. Prove that: int0^(pi//2)log|tanx+cotx|dx=pi(log)e2

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  18. Evaluate: int(pi//4)^(pi//4)log(sinx+cosx)dx

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  19. Evaluate: int0^pixlogsinxdx

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