### Home > APCALC > Chapter 6 > Lesson 6.3.2 > Problem6-94

6-94.

Your new derivative formulas can be reversed to enable you to integrate new expressions. Use your knowledge of basic derivative formulas to evaluate each of the following integrals. Homework Help ✎

1. $\int _ { 0 } ^ { 1 } ( \frac { 1 } { 1 + x ^ { 2 } } ) d x$

You should recognize the integrand. Think inverse trig!

1. $\int \frac { 4 } { \sqrt { 1 - y ^ { 2 } } } d y$

Refer to the hint in part (a).

1. $\int _ { 1 } ^ { e } ( \frac { 2 } { x } ) d x$

Before integrating, rewrite the integrand with a negative exponent.

1. $\int - \frac { 3 } { \sqrt { 1 - ( 3 t ) ^ { 2 } } } d t$

Refer to the hint in part (a).

There are two equivalent expressions for this integral.
It could $= \arccos(3t) + C$ or it could $= −\arcsin(3t) + C$.