IB Mathematics Applications & Interpretation Question Type 3: Calculating the Area Between a Polynomial in the Positive Section and the x Axis Exercises

Find the area under the curve $y=5x^4-2x^2+3$ from $x=-0.5$ to $x=1.5$.

Find the exact area under $y=e^x\cos x$ from $x=0$ to $x=\frac{\pi }{4}$.

Determine the area under $y=\ln (x+1)+x^2$ from $x=0$ to $x=1$.

Compute the area under $y=4-x^2$ from $x=-1$ to $x=1$.

Calculate the area under the curve $y=2x^2+3x+2$ between $x=0$ and $x=2$.

Calculate the area between the curve $y=x^5-x^3+2$ and the $x$-axis for $1\le x\le 2$.

Use technology to evaluate the definite integral ${\int }_0^1(e^x\ln (2x)-x^4)dx$. Give your answer correct to three decimal places.

Find the area bounded by the curve $y=x^3-6x^2+9x+1$ and the $x$-axis over the interval $[0,3]$.

Calculate the area under $y=e^{-x}\sin x$ from $x=0$ to $x=\frac{\pi }{2}$.

Determine the area under the curve $y=3x^3+x$ on $[0,2]$.

Compute the area under the curve $y=x{e}^x$ between $x=0$ and $x=1$.

Find the exact area under $y=e^{2x}-x^3$ from $0$ to $1$.