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Exercises for Question Type 3: Using technology to calculate indefinite integrals and area between curve and x-axis - IB | RevisionDojo

Question 1

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.

[5]

Question 2

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

\int_{0}^{4} \ln(1 + x^4)\,dx

[2]

Question 3

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.

[2]

Question 4

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.

[3]

Question 5

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

\int_{-2}^{2} e^{-x^2}\,dx

[2]

Question 6

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

[2]

Question 7

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

\int_{0}^{\pi} x \sin x \, \mathrm{d}x

[2]

Question 8

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

\int_{2}^{10} \frac{1}{\ln x}\,dx

[2]

Question 9

Approximate the definite integral $\int_{1}^{5}3x^2\ln(x)e^x\,dx$ to four decimal places using a graphing calculator.

[4]

Question 10

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.

[4]

Question 11

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.

[3]

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