Suggested languages for you:

Americas

Europe

Problem 10

Evaluate the given integral using the substitution (or method) indicated. $$ \int(x-1)^{2} e^{(x-1)^{3}} d x ; u=(x-1)^{3} $$

Expert verified

The short version of the answer is:
$$
\int (x-1)^2 e^{(x-1)^3}\, dx = \frac{1}{3} e^{(x-1)^3} + C
$$

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 13

The oxygen consumption of a turkey embryo increases from the time the egg is laid through the time the chick hatches. In a brush turkey, the oxygen consumption can be approximated by \(c(t)=-0.028 t^{3}+2.9 t^{2}-44 t+95\) milliliters per day $$ (20 \leq t \leq 50) $$ where \(t\) is the time (in days) since the egg was laid. \({ }^{46}\) (An egg will typically hatch at around \(t=50 .\) ) Use technology to estimate the total amount of oxygen consumed during the 21 st and 22 nd days \((t=20\) to \(t=22)\). Round your answer to the nearest 10 milliliters. HINT [See the technology note in the margin on page 996.]

Chapter 13

Evaluate the integrals. $$ \int_{2}^{3} \frac{x^{2}}{x^{3}-1} d x $$

Chapter 13

Evaluate the integrals. $$ \int_{-1}^{1}\left(2 x^{3}+x\right) d x $$

Chapter 13

If \(f\) is an increasing function of \(x\), then the left Riemann sum ________ (increases/decreases/stays the same) as \(n\) increases.

Chapter 13

Evaluate the integrals. $$ \int_{1}^{2} \frac{\sqrt{\ln x}}{x} d x $$

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner