Post Video Questions

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Please answer each of these questions to the best of your ability. You are welcome to re-watch parts of any of the videos to help you.

If $f$ is a continuous function and if $F^\prime (x) = f(x)$ for all real numbers $x$ , then $\int x \cdot f(x^2)\,dx =$

$F(x^2) + C$ $\frac {1}{x}F(x^2) + C$ $2F(x^2) + C$ $\frac {1}{2}F(x^2) + C$ $x \cdot F(x^2) + C$

Consider the integral $\int \frac {x\cdot \ln (x^2+4)}{3x^2+12}\,dx$ . Which part of this composite integrand would be appropriate to set equal to $u$ ?

$u = x^2+4$ $u = 3x^2+12$ $u = \ln (x^2+4)$ $u = x\cdot \ln (x^2+4)$ This integral cannot be evaluated using U-substitution.

Which of the following is equal to $\int (x^4-6x)^9\cdot (2x^3-3)\,dx$ ?

$\int u^9 \,du$ $2\int u^9\cdot u^{\prime }\,du$ $2\int u^9\,du$ $\frac {1}{2}\int u^9\,du$ $\frac {1}{2}\int u^9\cdot u^{\prime }\,du$