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Evaluate the following integral: int0^9f...

Evaluate the following integral: `int_0^9f(x)dx ,\ w h e r e\ f(x){sinx ,\ 0lt=xlt=pi//2 1,pi/2lt=xlt=3e^(x-3),\ 3lt=xlt=9`

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I=`int_0^(pi/2)sinx+int_(pi/2)^(3)1+int_3^(9)e^(x-3)dx`
=`[-cosx]_0^(pi/2)+[x]_(pi/2)^(3)+[e^(x-3)]_3^9`
=`1+3-pi/2+e^6-1`
=`3-pi/2+e^6`
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RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int(1//3)^1((x-x^3)^(1//3))/(x^4)dx

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  2. Evaluate the following integral: int0^(pi//2)sqrt(cos x-cos^3x)"\ "(se...

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  3. Evaluate the following integral: int0^9f(x)dx ,\ w h e r e\ f(x){sinx ...

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  4. Evaluate the following integral: int2^4f(x)dx ,\ w h e r e\ f(x)={7x+3...

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  5. Evaluate the following integral: int(-4)^4|x+2|dx

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  6. Evaluate the following integral: int(-1)^1|x+1|dx

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  7. Evaluate the following integral: int(-6)^6|x+2|dx

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  8. Evaluate the following integral: int1^2|x-3|dx

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  9. Evaluate the following integral: int1^(2pi)|s in x|dx

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  10. Evaluate the following integral: int2^8|x-5|dx

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  11. Evaluate the following integral: int0^4|x-1|dx

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  12. Evaluate the following integral: int0^4(|x|+|x-2|+|x-4|)dx\

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  13. Evaluate the following integral: int(-2)^2x e^(|x|)dx

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  14. Evaluate the following integral: int(-pi//2)^pisin^(-1)(sin x)dx

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  15. Evaluate the following integral: int(-3)^3|x+1|dx

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  16. Evaluate the following integral: int(-1)^2|2x+3|dx

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  17. Evaluate the following integral: int0^3|3x-1|dx

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  18. Evaluate the following integral: int(-2)^2|x+1|dx

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  19. Evaluate the following integral: int(-pi//4)^(pi//4)|s in x|dx

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  20. Evaluate the following integral: int(-pi//2)^(pi//2)|sinx+"cosx|dx

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