Question

(5 points) Evaluate the integral \begin{equation} \int_0^3 \int_y^3 \sin(x^2) \, dx \, dy \end{equation} by reversing the order of integration. With order reversed, \begin{equation} \int_a^b \int_c^d \sin(x^2) \, dy \, dx, \end{equation} where $a = 0$, $b = 9$, $c = x/3$, and $d = 3$. Evaluating the integral, $\int_0^3 \int_y^3 \sin(x^2) \, dx \, dy = 7/6 + \cos(81)/6$

          (5 points) Evaluate the integral \begin{equation*} \int_0^3 \int_y^3 \sin(x^2) \, dx \, dy \end{equation*} by reversing the order of integration. With order reversed, \begin{equation*} \int_a^b \int_c^d \sin(x^2) \, dy \, dx, \end{equation*} where $a = 0$, $b = 9$, $c = x/3$, and $d = 3$. Evaluating the integral, $\int_0^3 \int_y^3 \sin(x^2) \, dx \, dy = 7/6 + \cos(81)/6$

(5 points) Evaluate the integral
∫0^3 ^3 sin(x^2) dx dy
by reversing the order of integration. With order reversed,
^b ^d sin(x^2) dy dx,
where a = 0, b = 9, c = x/3, and d = 3. Evaluating the integral, ∫0^3 ^3 sin(x^2) dx dy = 7/6 + cos(81)/6

Added by Lindsey G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Tyler Moulton

07/21/2021

Step 1

Step 1: The original integral is $\int_0^3 \int_y^3 \sin(x^2) \, dx \, dy$. Show more…

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(5 points) Evaluate the integral $$ \int_0^3 \int_y^3 \sin(x^2) \, dx \, dy $$ by reversing the order of integration. With order reversed, $$ \int_a^b \int_c^d \sin(x^2) \, dy \, dx, $$ where $a = \boxed{0}$, $b = \boxed{9}$, $c = \boxed{x/3}$, and $d = \boxed{3}$. Evaluating the integral, $\int_0^3 \int_y^3 \sin(x^2) \, dx \, dy = \boxed{\frac{7}{6} + \frac{\cos(81)}{6}}$