Question:medium

If \(\int f(x) dx = F(x)\), then \(\int x^3 f(x^2) dx\) is equal to

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Use substitution \(t = x^2\) followed by integration by parts.

Updated On: Apr 7, 2026

\(\frac{1}{2}[x^2\{F(x)\}^2 - \int \{F(x)\}^2 dx]\)
\(\frac{1}{2}[x^2 F(x^2) - \int F(x^2) d(x^2)]\)
\(\frac{1}{2}[x^2 F(x) - \frac{1}{2}\int \{F(x)\}^2 dx]\)
None of the above

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The Correct Option is B

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Questions Asked in MET exam

If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then

MET - 2019
Continuity

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