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Using properties evaluate the following definite integrals,
evaluate the following: `int_2^8 |x-5|dx`

Text Solution

Verified by Experts

`|x-5|` = `{ x-5, x ge 5
-(x-5), x lt 5}`
therefore `int_2^8 |x-5| dx`
=`int_2^5 (5-x)dx + int_5^8 (x-5) dx`
=`(5x-x^2/2)_2^5 + (x^2/2 -5x)_5^8`
`(25-(25)/2)-(10-4/2)+((64)/2 - 40)-((25)/2 -25)`
`(25)/2-8-8+(25)/2 = 25-16 = 9`
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A N EXCEL PUBLICATION-INTEGRALS-QUESTION BANK
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  2. Evaluate the following int-5^5 abs[x+2]dx

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  3. Using properties evaluate the following definite integrals, evaluate ...

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  5. Evaluate. int0^(pi/4) log(1+tanx)dx

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  6. Find the following integrals. int0^2xsqrt(2-x)dx

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  7. Using properties evaluate the following definite integrals, evaluate ...

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  8. Using properties evaluate the following definite integrals, evaluate ...

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  9. Evaluate:int0^pix/(1+sinx)dx

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  10. Evaluate the following: int(-pi/2)^(pi/2)sin^7xdx

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  11. Using properties evaluate the following definite integrals, evaluate ...

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  12. Using properties evaluate the following definite integrals, evaluate...

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  13. Evaluateint0^pilog(1+cosx)dx

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  14. Using properties evaluate the following definite integrals, evaluate ...

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  15. Using properties evaluate the following definite integrals, evaluate...

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  16. Show that int0^a f(x) g(x) d x=2 int0^a f(x) d x, if f and g are defin...

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  17. Choose the correct answer int(-pi/2)^(pi/2) (x^3+x cosx+tan^5 x+1) dx ...

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  18. Choose the correct answer int0^(pi/2) log((4+3sinx)/(4+3cosx)) dx

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  19. Evaluate int-1^1 sin^5x cos^4x dx

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  20. Evaluate int(pi/6)^(pi/3) dx/(1+sqrttanx)

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