Chapter 6

Evaluate the definite integrals. $$ \int_{-1}^{0} e^{3 x} d x $$

Evaluate the definite integrals. $$ \int_{0}^{2} 2 t e^{t^{2}} d t $$

Evaluate the definite integrals. $$ \int_{-1}^{1}|x| d x $$

Evaluate the definite integrals. $$ \int_{-1}^{1} e^{-|s|} d s $$

Evaluate the definite integrals. $$ \int_{1}^{e} \frac{1}{x} d x $$

Evaluate the definite integrals. $$ \int_{2}^{3} \frac{1}{z+1} d z $$

Evaluate the definite integrals. $$ \int_{-2}^{-1} \frac{1}{1-u} d u $$

Evaluate the definite integrals. $$ \int_{2}^{3} \frac{2}{t-1} d t $$

Use l'Hospital's rule to compute $$ \lim _{x \rightarrow 0} \frac{1}{x^{2}} \int_{0}^{x} \sin t d t $$

Suppose that $$\int_{0}^{x} f(t) d t=2 x^{2}$$ Find \(f(x)\).

Suppose that \(\int_{0}^{x} f(t) d t=2 x^{2}\) Find \(f(x)\).

Suppose that $$\int_{0}^{x} f(t) d t=\frac{1}{2} \tan (2 x)$$ Find \(f(x)\).