QUIZIZZ 1.1 Integration of Functions

If $x^{10}+6$ is antiderivative of $10x^9$ , then find  $\int_{ }^{ }10x^9dx$    

•  $10x^9+k,\ where\ k=0$  

•  $x^{10}+k,\ where\ k=6$  

•  $9x^{10}+k,\ where\ k=6$  

•  $x^9+k,\ where\ k=0$  

Is $\left(x+x^2\right)^2$ the antiderivative of  $2x+6x^2+4x^3$ ? 

• Yes

• No

Find $\int_{ }^{ }\left(\frac{1}{\left(2x^2\right)^2}\right)dx$  

•  $12x^3+c$  

•  $-\frac{12}{x^3}+c$  

•  $\frac{x^3}{12}+c$  

•  $-\frac{1}{12x^3}+c$  

 $\int_{ }^{ }\left(\frac{4x-5}{\sqrt{x}}\right)dx$  

Find

•  $\frac{8}{3}x^{\frac{3}{2}}-10x^{\frac{1}{2}}+c$  

•  $\frac{4}{3}x^{\frac{1}{2}}+\frac{10}{\sqrt{x}}+c$  

•  $\frac{3}{8}x^{\frac{3}{2}}-5x^{\frac{1}{2}}+c$  

•  $\frac{4}{3}x^{\frac{1}{2}}+10^{\frac{3}{2}}+c$  

Given $f\left(x\right)=\frac{1}{x^3}$ and  $g\left(x\right)=x+\sqrt{x}$ . Find  $\int_{ }^{ }\left(f\left(x\right)-2g\left(x\right)\right)dx$   

•  $\frac{1}{x^2}-\frac{1}{3}x^2+\frac{4}{3}x^{\frac{3}{2}}+c$  

•  $\frac{1}{2x^2}-\frac{2}{3}x^2+4x^{\frac{3}{2}}+c$  

•  $-\frac{1}{2x^2}-x^2-\frac{4}{3}x^{\frac{3}{2}}+c$  

If p,q and r are constants, find $\int_{ }^{ }\left(px^2+\frac{1}{qx^2}+r\right)dx$  

•  $\frac{x^3}{3p}-\frac{1}{2qx}+rx+c$  

•  $\frac{px^3}{3}-\frac{1}{qx}+rx+c$  

•  $px^3+\frac{1}{qx}-rx+c$  

Evaluate $\int_{ }^{ }\left(\frac{\left(t^2-1\right)}{t+1}\right)dt$ 

Hint: Simplify the function before integrating 

•  $t^2-t+c$  

•  $\frac{t^2}{2}-t+c$  

•  $-\frac{t^2}{2}+t+c$  

•  $t^2+3t+c$  

Find $\int_{ }^{ }\frac{3}{\left(4-x\right)^3}dx$  

•  $\frac{3}{2\left(4-x\right)^2}+c$  

•  $\frac{-3}{4\left(4-x\right)^4}+c$  

•  $\frac{-3}{\left(4-x\right)^2}+c$  

 $\int_{ }^{ }\left(1-e^{-2t}\right)\left(2+e^{3t}\right)dt$  

•  $-2t+e^t-\frac{2e^{3t}}{3}-e^{2t}+c$  

•  $t-e^{2t}+\frac{e^{3t}}{4}-e^t+c$  

•  $2t^2+e^{-t}-\frac{e^{3t}}{3}-e^t+c$  

•  $2t+e^{-2t}+\frac{e^{3t}}{3}-e^t+c$  

Find $\int_{ }^{ }\left(6x-\frac{1}{2\sqrt{x}}\right)e^{\left(3x^2-\sqrt{x}\right)}dx$  

•  $3x^2-\sqrt{x}+c$  

•  $e^{\left(3x^2-\sqrt{x}\right)}+c$  

•  $e^{-3x^2+\sqrt{x}}+c$  

•  $6x-\frac{1}{2\sqrt{x}}+c$