Area between curves, integrating in y practice problems
Area between curves of the form x = g(y), integrating with respect to y. 10 problems with worked solutions; in 10 of them every
equation is proved by a computer algebra system.
3 worked problems
Try each one before opening the solution. Every line is labeled with what checked it. How we verify
\[ \int\limits_{-2}^{2} \left(4 - y^{2}\right)\, dy = \frac{32}{3} \]
A = ∫ (right − left) dy.✓ Proved
Answer \( \frac{32}{3} \)
✓ Nihil obstat Lines: 3 proved, 1 reviewed. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation. The full receipt ·
How we verify
\[ \int\limits_{-3}^{4} \left(- y^{2} + y + 12\right)\, dy = \frac{343}{6} \]
A = ∫ (right − left) dy.✓ Proved
Answer \( \frac{343}{6} \)
✓ Nihil obstat Lines: 3 proved, 1 reviewed. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation. The full receipt ·
How we verify
\[ \int\limits_{-2}^{2} \left(8 - 2 y^{2}\right)\, dy = \frac{64}{3} \]
A = ∫ (right − left) dy.✓ Proved
Answer \( \frac{64}{3} \)
✓ Nihil obstat Lines: 3 proved, 1 reviewed. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation. The full receipt ·
How we verify
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