Chapter 7

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{1}^{3} 5 d x $$

Find the integrals. $$ \int t e^{5 t} d t $$

Find the integrals in problems. Check your answers by differentiation. $$ \int 3 x^{2}\left(x^{3}+1\right)^{4} d x $$

Find an antiderivative. $$ f(x)=5 $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{0}^{4} 6 x d x $$

Find the integrals. $$ \int p e^{-0.1 p} d p $$

Find the integrals in problems. Check your answers by differentiation. $$ \int \frac{2 x}{x^{2}+1} d x $$

Find an antiderivative. $$ f(t)=5 t $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{1}^{2}(2 x+3) d x $$

Find the integrals. $$ \int(z+1) e^{2 z} d z $$

Find the integrals in problems. Check your answers by differentiation. $$ \int(x+10)^{3} d x $$

Find an antiderivative. $$ g(t)=t^{2}+t $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{0}^{2}\left(3 t^{2}+4 t+3\right) d t $$

Find the integrals. $$ \int y \ln y d y $$

Find the integrals in problems. Check your answers by differentiation. $$ \int x\left(x^{2}+9\right)^{6} d x $$

Find an antiderivative. $$ f(x)=x^{2} $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{1}^{2} \frac{1}{t^{2}} d t $$

Find the integrals. $$ \int x^{3} \ln x d x $$

Find the integrals in problems. Check your answers by differentiation. $$ \int 2 q e^{q^{2}+1} d q $$

Find an antiderivative. $$ f(x)=x^{4} $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{1}^{4} \frac{1}{\sqrt{x}} d x $$

Find the integrals. $$ \int q^{5} \ln 5 q d q $$

Find the integrals in problems. Check your answers by differentiation. $$ \int 5 e^{5 t+2} d t $$

Find an antiderivative. $$ g(t)=t^{7}+t^{3} $$

Find the integrals. $$ \int y \sqrt{y+3} d y $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{0}^{5} 3 x^{2} d x $$

Find the integrals in problems. Check your answers by differentiation. $$ \int t e^{t^{2}} d t $$

Find an antiderivative. $$ g(x)=6 x^{3}+4 $$

Find the integrals. $$ \int(t+2) \sqrt{2+3 t} d t $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{0}^{3} t^{3} d t $$

Find the integrals in problems. Check your answers by differentiation. $$ \int e^{-x} d x $$

Find an antiderivative. $$ f(q)=5 q^{2} $$

Find the integrals. $$ \int \frac{z}{e^{z}} d z $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{1}^{3} 6 x^{2} d x $$

Find the integrals in problems. Check your answers by differentiation. $$ \int t^{2}\left(t^{3}-3\right)^{10} d t $$

Find an antiderivative. $$ h(y)=3 y^{2}-y^{3} $$

Find the integrals. $$ \int \frac{\ln x}{x^{2}} d x $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{1}^{2} 5 t^{3} d t $$

Find the integrals in problems. Check your answers by differentiation. $$ \int x^{2}\left(1+2 x^{3}\right)^{2} d x $$

Find an antiderivative. $$ k(x)=10+8 x^{3} $$

Find the integrals. $$ \int \frac{y}{\sqrt{5-y}} d y $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{4}^{9} \sqrt{x} d x $$

Find the integrals in problems. Check your answers by differentiation. $$ \int x\left(x^{2}-4\right)^{7 / 2} d x $$

Find an antiderivative. $$ f(x)=3 x^{2}+5 $$

Find the integrals. $$ \int \frac{t+7}{\sqrt{5-t}} d t $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{0}^{1}\left(y^{2}+y^{4}\right) d y $$

Find the integrals in problems. Check your answers by differentiation. $$ \int x\left(x^{2}+3\right)^{2} d x $$

Find an antiderivative. $$ f(x)=x+x^{5}+x^{-5} $$

Find the integrals. $$ \int t \sin t d t $$

Using the Fundamental Theorem, evaluate the definite integrals in problem exactly. $$ \int_{1}^{2} \frac{1}{2 t} d t $$