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Evaluate the following definite integral...

Evaluate the following definite integral: `int_0^1sqrt(x)dx`

Text Solution

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Taking, `I=int_{0}^{1} sqrt{x} dx`
` I=[frac{2 x^{32}}{3}]_{0}^{1}`
` I=frac{2}{3}`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following definite integral: int1^2(x+3)/(x(x+2))dx

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  2. Evaluate the following definite integral: int0^2 1/(4+x-x^2)dx

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  3. Evaluate the following definite integral: int0^1sqrt(x)dx

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  4. Evaluate the following definite integral: int0^4 1/(sqrt(4x-x^2))dx

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  5. Evaluate the following definite integral: int1^4(x^2+x)/(sqrt(2x+1))dx

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  6. Evaluate the following definite integral: int1^2((x-1)/(x^2))e^x dx

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  7. Evaluate the following definite integral: int0^1(x e^x+cos(pix)/4)dx

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  8. Evaluate the following definite integral: int0^(2pi)e^(x//2)sin(x/2+pi...

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  9. Evaluate the definite integrals int0^1 (dx)/(sqrt(1+x)-sqrt(x))

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  10. Evaluate the following definite integral: int1^2e^(2x)(1/x-1/(2x^2))dx

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  11. Evaluate the following definite integral: int0^(pi//2)x^2sinx\ dx

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  12. Evaluate the following definite integral: int0^(pi//2)cos^2x\ dx

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  13. Evaluate the following definite integral: int1^2logx\ dx

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  14. Evaluate the following definite integral: int1^e(e^x)/x(1+x log x)dx

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  15. Evaluate : inte^(e^2){1/(logx)-1/((logx)^2)}dx

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  16. Evaluate the definite integrals int0^1(2x+3"")/(5x^2+1)dx

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  17. Evaluate the following definite integral: int0^1 1/(2x^2+x+1)dx

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  18. Evaluate the following definite integral: int0^2 1/(sqrt(3+2x-x^2))dx

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  19. Evaluate the following definite integral: int(-1)^1 1/(x^2+2x+5)dx

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  20. Evaluate : int0^1x(1-x)^5dx

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