Home > CALC > Chapter 6 > Lesson 6.4.3 > Problem6-158

6-158.

Use the relationship between differentiation and integration to simplify the following problems.

As you work through this set of problems, look for patterns.

1. $\frac { d } { d x } ( \operatorname { cos } ( 3 x ^ { 2 } ) )$

Chain Rule.

1. $\int 6 x \operatorname { sin } ( 3 x ^ { 2 } ) d x$

This one is tricky. Concentrate on the $3x^²$ part of the integrand. What will happen when you anti-differentiate that part?

Refer to part (a) (the question, not the hint).

1. $\frac { d } { d x } ( \sqrt { 3 x ^ { 9 } - 5 x } )$

Before you differentiate, rewrite the expression as with a fractional exponent.

1. $\int \frac { 27 x ^ { 8 } - 5 } { \sqrt { 3 x ^ { 9 } - 5 x } } d x$

A clue is directly above (in part (c)).
And don't forget the $+C$.