Question

Evaluate the integral. \[ \int_{0}^{3} \int_{0}^{e^{x}} 4 \sqrt{1+e^{x}} d y d x= \] \( \square \)

          Evaluate the integral.
\[
\int_{0}^{3} \int_{0}^{e^{x}} 4 \sqrt{1+e^{x}} d y d x=
\]
\( \square \)

Evaluate the integral.

∫0^3∫0^e^x 4 √(1+e^x) d y d x=

□

Added by Kathryn U.

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 7

Instant Answer

Solved by Expert Bradley Duda

Step 1

The inner integral is: \[ \int_{0}^{e^{x}} 4 \sqrt{1+e^{x}} \, dy \] Since \( 4 \sqrt{1+e^{x}} \) is constant with respect to \( y \), the integral becomes: \[ 4 \sqrt{1+e^{x}} \int_{0}^{e^{x}} \, dy = 4 \sqrt{1+e^{x}} \cdot [y]_{0}^{e^{x}} \] Show more…

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