Integration

What can integration be used for?

• To calculate the profit and loss in business using graphs

• To determine the speed or distance covered by something

• To find areas, volumes, central points

• To identify variation in temperatures

 $\int\left(4x^2-2x+3\right)dx=?$  

•  $x^2\left(\frac{4x}{3}-1\right)+3x+C$  

•  $x^2\left(\frac{3x}{4}-1\right)+3x+C$  

•  $x^2\left(\frac{2x}{3}-1\right)-3x+C$  

•  $x^2\left(\frac{3x}{2}-1\right)-3x+C$  

 $\int\left(5x^2-8x+5\right)dx=?$  

•  $\frac{5x^4}{4}-4x^2+5x+C$  

•  $\frac{5x^3}{3}-4x^2+5x+C$  

•  $\frac{5x^3}{3}+4x^2+5x+C$  

•  $\frac{5x^3}{3}-8x^2+5x+C$  

 $\int_2^4\left(x^3+8x-12\right)dx=?$  

• 132

• 84

• 36

• -12

 $\int\left(7\sin x\right)dx=?$  

•  $-7\cos x+C$  

•  $-7\sin x+C$  

•  $7\cos x+C$  

•  $7\sin x+C$  

 $\int\left(6\cos3\theta\right)d\theta=?$  

•  $-6\sin3\theta+C$  

•  $6\sin3\theta+C$  

•  $-2\sin3\theta+C$  

•  $2\sin3\theta+C$  

 $\int\left(\left(1+4x^2\right)x\right)dx=?$  

•  $x^2+x^4+C$  

•  $\frac{x^2}{2}+x^3+C$  

•  $\frac{x^2}{2}+x^4+C$  

•  $x+\frac{4x^3}{3}+C$  

 $\int\left(\frac{3x^2+x\sqrt{x}}{x^2}\right)dx=?$  

•  $3x+\frac{1}{2}\sqrt{x}$  

•  $3x+2\sqrt{x}$  

•  $3x+\frac{1}{2}\sqrt{x}+C$  

•  $3x+2\sqrt{x}+C$  

 $\int\left(\frac{5}{x}+\frac{3}{x^2}-\frac{8}{x^3}\right)=?$  

•  $5+\frac{3}{x}-\frac{4}{x^2}+C$  

•  $5-\frac{3}{x}+\frac{4}{x^2}+C$  

•  $5\ln\left(x\right)-\frac{3}{x}+\frac{4}{x^2}+C$  

•  $5\ln\left(x\right)+\frac{3}{x}-\frac{4}{x^2}+C$  

Find the area of the shaded region.

• $\frac{63}{6}units^2$

• $\frac{52}{3}units^2$

• $\frac{32}{3}units^2$

• $\frac{25}{3}units^2$