Question

9. Use a change of variables to evaluate the following definite integral.\\ $\int_0^2 \frac{2x}{(x^2+4)^3} dx$\\ Determine a change of variables from $x$ to $u$. Choose the correct answer below.\\ A. $u = x^2 + 4$\ B. $u = x^2$\ C. $u = 2x$\ D. $u = (x^2 + 4)^3$\\ Write the integral in terms of $u$.\ $\int_0^2 \frac{2x}{(x^2+4)^3} dx = \int_4^{ } \text{ } du$\\ Evaluate the integral.\ $\int_0^2 \frac{2x}{(x^2+4)^3} dx = $\ (Type an exact answer.)

          9. Use a change of variables to evaluate the following definite integral.\\
$\int_0^2 \frac{2x}{(x^2+4)^3} dx$\\
Determine a change of variables from $x$ to $u$. Choose the correct answer below.\\
A. $u = x^2 + 4$\
B. $u = x^2$\
C. $u = 2x$\
D. $u = (x^2 + 4)^3$\\
Write the integral in terms of $u$.\
$\int_0^2 \frac{2x}{(x^2+4)^3} dx = \int_4^{ } \text{ } du$\\
Evaluate the integral.\
$\int_0^2 \frac{2x}{(x^2+4)^3} dx = $\
(Type an exact answer.)

9. Use a change of variables to evaluate the following definite integral.

∫0^2 (2x)/((x^2+4)^3) dx

Determine a change of variables from x to u. Choose the correct answer below.

A. u = x^2 + 4B. u = x^2C. u = 2xD. u = (x^2 + 4)^3

Write the integral in terms of u.∫0^2 (2x)/((x^2+4)^3) dx = ∫4^ du

Evaluate the integral.∫0^2 (2x)/((x^2+4)^3) dx =(Type an exact answer.)

Added by Derrick D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Babita Kumari

Step 1

In this case, we can let u = x + 4. To find the differential du, we can differentiate both sides of the equation u = x + 4 with respect to x: du/dx = 1 Now, we can solve for dx: dx = du Substituting this into the original integral, we have: ∫(2x/(x+4)) dx = Show more…

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Use a change of variables to evaluate the following definite integral: âˆ«(2x/(x+4)) dx Determine a change of variables from x to u. Choose the correct answer below. A. u = x^2 + 4 B. u = x^2 C. u = 2x D. b+ = naO Write the integral in terms of u: âˆ«(2x/(x+4)) dx = âˆ«(2u/(u+4)) du Evaluate the integral: âˆ«(2u/(u+4)) du (Type an exact answer.)