http://www.ck12.org Chapter 7. Integration Techniques
Review Questions
Evaluate the following integrals.
1.∫x (^21) − 1 dx
2.∫x (^2) −x 2 x− 3 dx
3.∫x (^3) +x^12 − 2 xdx
4.∫x 2 x+^34 dx
5.∫ (^011) +φφdφ
6.∫ (^15) x 2 x(−x+^11 )dx
7. Evaluate the integral by making the properu−substitution to convert to a rational function:∫sin (^2) θ+cos4 sinθθ− 5 dθ.
Evaluate the integral by making the properu−substitution to convert to a rational function:∫e 23 θe−θ 1 dθ.
Find the area under the curvey= 1 /( 2 +ex),over the interval[−ln3,ln4].(Hint: make au−substitution to
convert the integrand into a rational function.)
Show that∫a (^2) −^1 x 2 dx= 21 aln∣∣aa−+xx∣∣+C.