IB Mathematics Analysis and Approaches Topic SL…

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

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

(b) Show that $g''(x)=-4g(x)$ .

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

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

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

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

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

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

(a) The expression $2 \sqrt{x}+\frac{3}{\sqrt{x}}$ can be written as $2 x^{p}+3 x^{q}$ . Write down the values of $p$ and $q$ .

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

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

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

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

(c) 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.

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