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Evaluate the following definite integr...

Evaluate the following definite integrals as limit of sums. `int_0 ^4(x+e^(2x))dx`

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We have `int_0^4(x+e^(2x))dx`​
⇒`int_0^4xdx+int_0^4e^(2x)dx`​
⇒`1/2int_0^4[x^2]​+1/2​int_0^4[e^(2x)]+c`​
⇒`1/2​×16+1/2​[e^8−1]+c`​
`=>8+1/2​[e^8−1]+c.`​
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integrals as limit of sum: int0^(pi//2)cosx\ dx

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  2. Evaluate the following integrals as limit of sum: int0^2(3x^2-2)dx

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  3. Evaluate the following definite integrals as limit of sums. int0 ^4(...

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  4. Evaluate int0^2(x^2+\ 2x+1)dx as limit of a sum.

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  5. Evaluate the following definite integrals as limit of sums. inta^ b ...

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  6. Evaluate the following integrals as limit of sum: int2^3x^2dx

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  7. Evaluate the following definite integrals as limit of sums. int2 ^3x...

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  8. Evaluate the following integrals as limit of sum: int0^2(x^2-x)dx

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  9. Evaluate the following integrals as limit of sum: int1^3(3x^2+1)dx

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  10. Evaluate the following integrals as limit of sum: int0^1(3x^2+5x)dx

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  11. Evaluate the following integrals as limit of sum: int0^2 e^x dx

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  12. Evaluate the following integrals as limit of sum: int0^(pi//2)sinx\ dx

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  13. Evaluate the following definite integrals as limit of sum: int0^2(x^2+...

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  14. Evaluate the following integrals as limit of sum: int1^4(3x^2+2x)dx

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  15. Evaluate the following integral: int0^2(x^2+x)dx

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  16. Evaluate the following integrals as limit of sum: int0^(3.)(2x^2+3x+5)...

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  17. Evaluate the following definite integrals as limit of sums. int0 5(...

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  18. Evaluate the following definite integrals as limit of sums. int1 4(...

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  19. Evaluate: int1^3(2x^2+5x)dx\ "a s\ l i m i t\ o f\ a\ sum"dot

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  20. Evaluate each of the following integral: int0^(pi//2)sin^2x\ dx

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