Question Type 3: Using technology to calculate indefinite integrals and area between curve and x-axis Bootcamps

Using technology, evaluate the definite integral 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.

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

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:

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

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

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.

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

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.