Question

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

Answer 1

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