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Math Help - cal 2

  1. #1
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    cal 2

    intergral x(x^2-9)^3 dx
    intergral with limits 3/2 and 0 xsin(x^2)dx give answer in decimal number.
    intergral with limits 4 and -2 x^2(x^3 + 8)^2dx. give answer in decimal number.
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  2. #2
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    Quote Originally Posted by lay137 View Post
    intergral x(x^2-9)^3 dx
    \int x(x^2-9)^3 dx
    Use u=x^2-9.
    Then you get,
    \frac{1}{2} \int u^3 du
    \frac{1}{2} \cdot \frac{1}{4}u^4 +C
    \frac{1}{8}u^4+C
    \frac{1}{8}(x^2-9)^4+C

    intergral with limits 3/2 and 0 xsin(x^2)dx give answer in decimal number.
    \int_0^{3/2} x\sin x^2 dx
    Let u=x^2 then,
    \frac{1}{2}\int_0^{9/4} \sin u du
    \frac{1}{2} \left( -\cos u \big|_0^{9/4} \right)
    You can evaluate that.
    intergral with limits 4 and -2 x^2(x^3 + 8)^2dx. give answer in decimal number.
    \int_{-2}^4 -2 x^2(x^3+8)^2 dx
    Let u=x^3+8 then,
    \frac{1}{3}\int_0^72 -2 u^2 du
    \frac{1}{3} \left( \frac{-2}{3} u^3 \big|_0^{72} \right)
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