Introduction to Integrals

Evaluate:  $\int2x\ dx$  

•  $2x+C$  

•  $2+C$  

•  $x^2+C$  

•  $\frac{2x^3}{3}+C$  

Evaluate  $\int5x^3+2x\ \ dx$  

•  $15x^2+2+C$  

•  $5x^4+2x^2+C$  

•  $\frac{1}{5}x^4+\frac{1}{2}x^2+C$  

•  $\frac{5}{4}x^4+x^2+C$  

Evaluate  $\int\sin x\ dx$  

•  $\cos x\ +C$  

•  $-\cos x+C$  

•  $-\sin x+C$  

•  $\frac{1}{2}\sin x^2+C$  

Let  $f\left(x\right)=\frac{6}{x^2}$  be a differential equation.  Find the general solution.

•  $F\left(x\right)=\frac{18}{x^3}+C$  

•  $F\left(x\right)=-\frac{12}{x}+C$  

•  $F\left(x\right)=-\frac{6}{x}+C$  

•  $F\left(x\right)=-\frac{2}{x^3}+C$  

Which of the following will give a displacement function as a general solution? Note:  a(t) is an acceleration function, v(t) is a velocity function, and s(t) is a displacement function.

•  $\int v\left(t\right)dt$  

•  $\int a\left(t\right)dt$  

•  $\int s\left(t\right)\ dt$  

•  $\int a'\left(t\right)dt$  

Evaluate  $\int\sqrt{x}dx$  

•  $x^{\frac{1}{2}}+C$  

•  $\frac{1}{2}x^{-\frac{1}{2}}+C$  

•  $x^{\frac{3}{2}}+C$  

•  $\frac{2}{3}x^{\frac{3}{2}}+C$  

Evaluate  $\int7x-9x_{ }^{-3}-2\ \ dx$  

•  $F\left(x\right)=7+27x^{-4}+C$  

•  $F\left(x\right)=\frac{7}{2}x^2+\frac{9}{2}x^{-2}-2x+C$  

•  $F\left(x\right)=7x^2-9x^{-2}-2x+C$  

•  $F\left(x\right)=7x^0-9x^{-4}-2x^{-1}+C$  

Evaluate  $\int e^xdx$  

•  $2e^{2x}+C$  

•  $e^{2x^2}+C$  

•  $e^{\frac{1}{2}x^2}+C$  

•  $e^x+C$  

Evaluate  $\int\ \frac{1}{x}\ dx$  

•  $\ln x+C$  

•  $e^x+C$  

•  $1+C$  

•  $e^{-x}+C$  

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