If int f(x) dx = g(x),then int f(x) g(x) dx i | vedclass

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(B) Given that $\int f(x) dx = g(x)$.This implies that $f(x) = g'(x)$.We need to evaluate the integral $\int f(x) g(x) dx$.Substituting $f(x) = g'(x)$

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$\frac{1}{2} g^{2}(x)$

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(B) Given that $\int f(x) dx = g(x)$.This implies that $f(x) = g'(x)$.We need to evaluate the integral $\int f(x) g(x) dx$.Substituting $f(x) = g'(x)$,we get $\int g'(x) g(x) dx$.Let $g(x) = u$,then $g'(x) dx = du$.The integral becomes $\int u du = \frac{u^2}{2} + C$.Substituting back $u = g(x)$,we get $\frac{1}{2} g^2(x) + C$.

If $\int f(x) dx = g(x)$,then $\int f(x) g(x) dx$ is equal to

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