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anonymous

  • 5 years ago

how to solve ∫sin(5x + 2) dx?

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  1. anonymous
    • 5 years ago
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    Do you know how to do u-substitution?

  2. anonymous
    • 5 years ago
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    if u=5x+2, du=5 dx... \[\int\limits_{}^{}\sin(u)du\]

  3. anonymous
    • 5 years ago
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    sin(nx)dx= -1/n cos(nx)+c

  4. anonymous
    • 5 years ago
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    f'(x)=cos(u)5?

  5. anonymous
    • 5 years ago
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    As an antiderivative, we should be able to differentiate our final answer and obtain the original equation, that is, sin(5x+2). if u = 5x+2 and du = 5dx, we substitute in like this: \[1/5\int\limits_{}\sin (u) du\] Note that since du = 5dx, we need to cancel out the 5. Hence the 1/5. The integral of the sine function is -cos. So we have 1/5 (-cos(u)) +c Replacing for u, we have 1/5 -cos(5x+2)+c Now lets differentiate and check our work... 1/5 * 5 * sin(5x+2) + 0 = 1*sin(5x+2) = sin(5x+2)

  6. anonymous
    • 5 years ago
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    thank you :)

  7. shadowfiend
    • 5 years ago
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    Don't forget to give peddani a medal if she was helpful! :)

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