Techniques of Integration

Evaluate. (Be sure to check by differentiating!) \[ \int\left(4 t^{3}-7\right) t^{2} d t \] Determine a change of variables from $t$ to $u$. Choose the correct answer below. A. $u=4 t-7$ B. $u=t^{2}-7$ C. $u=4 t^{3}-7$ D. $u=t^{2}$ Write the integral in terms of $u$. \[ \int\left(4 t^{3}-7\right) t^{2} d t=\int(\square) d u \] (Type an exact answer. Use parentheses to clearly denote the argument of each function.) Evaluate the integral. \[ \int\left(4 t^{3}-7\right) t^{2} d t= \] (Type an exact answer. Use parentheses to clearly denote the argument of each function.)

Evaluate the indefinite integral \[ \int 8 \sin ^{6} x \cos x d x= \]

Find $\frac{d y}{d r}$ for $y=\int_{0}^{r} \sqrt{11+12 t^{2}} d t$

Evaluate the integral $\int_{1}^{\sqrt{2}} \frac{s^{2}+\sqrt{s}}{s^{2}} d s$