### Home > APCALC > Chapter 6 > Lesson 6.4.1 > Problem6-118

6-118.

Without a calculator, evaluate the following integrals.

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1. $\int _ { - 2 } ^ { 1 } ( 10 x - 3 ) d x$

Visualize the graph of this integrand.

1. $\int _ { 0 } ^ { \pi / 3 } \operatorname { sec } ( x ) \operatorname { tan } ( x ) d x$

Think! Reciprocal trig functions...

1. $\int _ { 9 } ^ { 25 } \sqrt { x } d x$

Before you integrate, rewrite the integrand as a power function.

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

If $f\left(x\right)=\ln\left(x\right),$ then $F\left(x\right)=x\ln\left(x\right)−x+C$

1. $\int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { 1 - x ^ { 2 } } } d x$

Think! Inverse trig functions...