Practice Area Bounded By Curves And Axes (7.3)

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8 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Find the area under the curve $y = x^3$ from $x = 0$ to $x = 1$ .
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Remember to integrate \$ x^3 \$.
Question 2.
Calculate the area under the curve $y = 2x$ from $x = 0$ to $x = 3$ .
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Integrate using basic power rule.
3Question 3.
What is the formula to calculate the area bounded by a curve and the x-axis?
- \$ \\int_a^b f(x) \\, dx \$
- \$ \\int_a^b |f(x)| \\, dx \$
- \$ |f(x)| \\, dx \$
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Think about when a curve is below the x-axis.
4Question 4.
True or False: The area between two curves is the integral of the upper function minus the lower function.
- True
- False
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Which function is on top?
Question 5.
Find the area bounded by the curve $y = \ln(x)$ , the x-axis, and the lines $x = 1$ and $x = e$ .
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Use integration by parts for \$ \\ln(x) \$.
Question 6.
Determine the area between the curves $y = x^3$ and $y = -x$ from their points of intersection.
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Find the intersection points before integrating!

4 more questions in this section. Enroll free to practise them all.