IB Mathematics Analysis and Approaches Topic SL…

Let $g(x)=\frac{\sin(2x)}{2}\left(\frac{1}{\tan(x)}+2\right)-\sin^2(x)$ .

Show that $g(x)=\sin(2x)+\cos(2x)$ .

Define $g(x)=\sin ^{-1}\left(\frac{x}{3}\right)+\cos ^{-1}\left(\frac{x}{3}\right)$ for , and .

Find $\int\left(4 x^{2}-3 x+2\right) d x$ .

The expression $2 \sqrt{x}+\frac{3}{\sqrt{x}}$ can be written as . Write down the values of and .

Let $g(x)=x^3-4x+5$ .

Hence, using your answer from Part 2, find $\int\!g(x)\,dx$ in terms of $g'(x)$ .

Show that $g(x)=\frac{\pi}{2}$ for all $x \in[-3,3]$ .

Find the exact coordinates of the intersection of $h$ and the line $y=2 x+1$ .

Find the exact coordinates of the point where the normal to the curve $y=h(x)$ at $x=1$ intersects the $x$ -axis.

Find the exact area of the region bounded by $h, y=2 x+1$ , and the $y$ -axis.

Given $f^{\prime}(x)=4 x^{2}-3 x+2$ and $f(2)=5$ , find $f(x)$ .

the area under the curve $y=4 x^{2}-3 x+2$ from $x=0$ to $x=1$ .

Find $\int\left(2 \sqrt{x}+\frac{3}{\sqrt{x}}\right) d x$ .

the curve $y=2 \sqrt{x}+\frac{3}{\sqrt{x}}$ for $0.5 \leq x \leq 2$ , indicating the approximate shape and the coordinates of at least one point on the curve.

Find $\int g(x)\,dx$ .

Given $f'(x)=g(x)$ and $f(2)=5$ , find $f(x)$ .

the area under the curve $y=g(x)$ from $x=-1$ to $x=1$ .

IB Mathematics Analysis and Approaches SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank

IB Mathematics Analysis and Approaches SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank

IB Mathematics Analysis and Approaches SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank

IB Mathematics Analysis and Approaches SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 5.5—integration Introduction, Areas Between Curve and x Axis Questionbank