Sue Pemberton Solutions for Chapter: Integration, Exercise 6: EXERCISE 9F

The diagram shows the curve $y=\sqrt{2x+1}$. The shaded region is bounded by the curve, the $y-$axis and the line $y=3$, Find the area of the shaded region.

Find the area of the region bounded by the curve $y=2x^2+1$, the line $y=9$ and the $y-$axis.

Find the area of the region enclosed by the curve $y=\frac{12}{x^2}$, the $x-$axis and the lines $x=1$ and $x=4$.

The line $x=p$ divides the area under curve $y=\frac{12}{x^2}$, $x-$axis and the lines $x=1$ and $x=4$ into two parts of equal area. Find the value of $p$.

Find the shaded area enclosed by the curve $y=2\sqrt{x}$, the line $x+y=8$ and the $x-$axis.       [Enter the value excluding units]

The diagram shows the curve $y=\sqrt{2x+1}$ that intersects the $x-$axis at $A$. The normal to the curve at $B(4,3)$ meets the $x-$axis at $C$. Find the area of the shaded region.        [Enter the value excluding units]

The figure shows part of the curve $y=f\left(x\right)$. The points $P(2,4)$ and $Q(7,12)$ lie on the curve. Given that ${\int }_2^{7}y \mathrm{d}x=42$, find the value of ${\int }_4^{12}x \mathrm{d}y$.        [Enter the value excluding units]

The figure shows part of the curve $y=g\left(x\right)$. The points $A(2,8)$ and $B(6,1)$ lie on the curve. Given that ${\int }_2^{6}y \mathrm{d}x=16$, find the value of ${\int }_1^{8}x \mathrm{d}y$.       [Enter the value excluding units]