Question

(Image included) is the graph of y=x^2+5.

The area bounded by y=x^2+5 and the x-axis from x=1 to x=5 is?

Answer 1

`\displaystyle\\A=\int\liomits_1^5(x^2+5)=\left[(x^3)/(3)+5x\right]_1^5=(5^3)/(3)+5\cdot5-\left((1^3)/(3)+5\cdot1\right)=(125)/(3)+25-\left((1)/(3)+5\right)=(125)/(3)+(75)/(3)-\left((1)/(3)+(15)/(3)\right)=(200)/(3)-(16)/(3)=(184)/(3)`