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Math Help - Fundamental Theorem of Calculus

  1. #1
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    Exclamation Fundamental Theorem of Calculus

    if f(x) = \int from 0 to x of (x^2)*(sin(t^2)) dt, find f'(x)

    i wanna believe that it is just (x^2)*(sin(x^2)) but it seems like that is too simple of an answer since I'm doing this in the problems plus section of chapter five.
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  2. #2
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    Quote Originally Posted by CalculusABStudent View Post
    if f(x) = \int from 0 to x of (x^2)*(sin(t^2)) dt, find f'(x)

    i wanna believe that it is just (x^2)*(sin(x^2)) but it seems like that is too simple of an answer since I'm doing this in the problems plus section of chapter five.
    Assuming the x^2 is NOT a typo, then you can re-write the function as f(x) = x^2 \int_0^x \sin(t^2) \, dt. Now use the product rule.

    If it IS a typo, then the obvious answer is correct.
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  3. #3
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    not a typo.
    and thankyou!
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  4. #4
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    x^2 (sin⁡(x^2 ) )+∫_0^x▒〖sin⁡(t^2 )dt〗(2x)
    is that the answer?
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  5. #5
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    Yes.
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