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Evaluate the following definite integr...

Evaluate the following definite integrals as limit of sums. `int_0 ^5(x+1)""dx`

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We have,` int_0^5​(x+1)dx`
`=lim_(N->oo) h[sum_(i=0)^(n-1)f(a+r.h)]]`
`=lim_(N->oo) (5/n)[sum_(i=0)^(n-1)(r(5/n)+1)]]`
Since `h=5/n`
=`5/n`
=`lim_(N->oo) [sum_(i=0)^(n-1) (25/n^2)*​r+(5/n)​(.n−1)]`
=`lim_(N->oo)[(25/n^2)*​n.(n-1]/2+(5/n)​(n−1)]`
=`25/2​+5`
=`35/2`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
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  2. Evaluate the following integrals as limit of sum: int1^3(3x-2)dx

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

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  4. Evaluate the following integrals as limit of sum: int3^5(2-x)dx

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  5. Evaluate the definite integrals as limit of sums int1^2x^2dx

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  6. Evaluate the following integrals as limit of sum: int1^2(x^2-1)dx

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

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  8. Evaluate the following integrals as limit of sum: int(-1)^1(x+3)dx

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

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

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

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  12. Evaluate the following integrals as limit of sum: int2^3(2x^2+1)dx

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  13. Evaluate the following integrals as limit of sum: int0^2(x^2+4)dx

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

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

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  16. Evaluate the following integrals using limit of sum. int(a)^(b)cos x...

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

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

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

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

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