IB Mathematics Analysis and Approaches Question Type 3: Using Technology to Calculate Indefinite Integrals and Area Between Curve and X-axis Exercises

Using technology, find the total area between the curve $y=x\sin x$ and the $x$-axis on $[0,2\pi ]$. Give your answer to 3 decimal places.

Using technology, evaluate the definite integral to 3 decimal places:

$${\int }_0^4\ln (1+x^4)dx$$

Evaluate the definite integral $${\int }_2^{4}3x^2\ln (x)e^{x}dx$$ using a calculator and give the result to three decimal places.

Use a graphing calculator to sketch $y=3x^2\ln (x)e^{-x}$ on the domain $[1,5]$ and estimate the $x$-coordinate of its local maximum.

Using technology, evaluate the definite integral to 3 decimal places:

$${\int }_{-2}^2{e}^{-x^2}dx$$

Use a graphing calculator to approximate $${\int }_3^{6}3x^2\ln (x)e^{x}dx$$ to four significant figures.

Using technology, evaluate the definite integral to 3 decimal places:

$${\int }_0^{\pi }x\sin x\mathrm{d}x$$

Using technology (radians), evaluate to 3 decimal places:

$${\int }_2^{10}\frac{1}{\ln x}dx$$

Approximate the definite integral $${\int }_1^{5}3x^2\ln (x)e^{x}dx$$ to four decimal places using a graphing calculator.

Using technology, find the total area between the curve $y=(x-1)e^{-x^2}$ and the $x$-axis on $[-1,3]$. Give your answer to 3 decimal places.

Using technology, find the total area between the curve $y=e^x-2$ and the $x$-axis on $[0,2]$. Give your answer to 3 decimal places.