do number 1 please **Transcription for Educational Content:**1. Use a Riemann sum with \( m = 3 \) and \( n = 2 \) to estimate the value of \(\iint_R (x + 2y) \, dA\) where \( R = [0, 6] \times [0, 2] \). Take sample points to be the lower right corners.2. Compute \(\int_0^1 \int_0^1 \frac{ye^{y^2}}{1 + x^2} \, dx \, dy\).3. Compute \(\int_0^1 \int_0^1 e^{-x^2} 3xy^2 \, dy \, dx\).4. Compute \(\int_0^1 \int_x^y \int_x^y 6xyz \, dz \, dx \, dy\).5. Compute \(\int_0^1 \int_x^1 \cos(y^2) \, dy \, dx\) by reversing the order of integration.6. Find the volume of the solid bounded by the paraboloids \( z = x^2 + y^2 \) and \( z = 2 - x^2 - y^2 \).7. Compute \(\int_0^1 \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \frac{xy}{\sqrt{x^2 + y^2}} \, dy \, dx\) by converting to polar coordinates.8. Find the \( x \)-coordinate of the center of mass of the lamina that occupies the region \( D = \{(x, y) \mid 0 \leq x \leq 1, x^2 \leq y \leq 1\} \) and has density function \(\rho(x, y) = x + y\).9. Find the surface area of the part of the cylinder \( y^2 + z^2 = 9 \) that is above the rectangle \( R = [0, 2] \times [-3, 3]\).10. Compute \(\int_0^1 \int_0^4 \int_0^2 e^{0.5x + y - z} \, dz \, dy \, dx

Name: do number 1 please **Transcription for Educational Content:**1. Use a
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: do number 1 please **Transcription for Educational Content:**1. Use a Riemann sum with \( m = 3 \) and \( n = 2 \) to estimate the value of \(\iint_R (x + 2y) \, dA\) where \( R = [0, 6] \times [0, 2] \). Take sample points to be the lower right corn