Calculus 3

Given an iterated integral with a function having $y^5 + 1$ in the denominator, reverse the order of integration to simplify the integral.

Find the volume of the solid bounded by the surfaces $z = y + 1$ and $z = x^2 + 1$ over the region where $y = x^2$ and $y = 1$.

Find the area bounded by the curves $y = x^2$ and $x = 4$ using the double integral technique.

Solve a double integral problem using the Fundamental Theorem of Calculus.

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Compute the volume under the surface given by $f(x, y) = 9 - x^2 - y^2$ over the rectangular region where $x$ is between $-2$ and $2$ and $y$ is between $-2$ and $2$.

Set up a generic integral for the region bounded by the curves $y = 4x$ and $y = x^3$, using the order of iteration $dy/dx$.

Given an iterated integral with a function having $y^5 + 1$ in the denominator, reverse the order of integration to simplify the integral.

Find the volume of the solid bounded by the surfaces $z = y + 1$ and $z = x^2 + 1$ over the region where $y = x^2$ and $y = 1$.

Find the area bounded by the curves $y = x^2$ and $x = 4$ using the double integral technique.

Solve a double integral problem using the Fundamental Theorem of Calculus.

Find the volume under the surface $f(x, y) = 1 + 4xy$ where $x$ ranges from 0 to 1 and $y$ ranges from 1 to 3.

Find the volume under the surface $f(x, y) = 3x^{2} - 3xy^{2}$ over the region bounded by $y = x^{2}$ and $y = 2x$.

Solve a double integral problem involving a function of two variables over a specified domain.