please do question 5 Sure, here's the transcription suitable for an educational website:---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 \(\int_{-1}^2 \int_0^1 \frac{y e^y}{1 + x^2} \, dx \, dy \).3. Compute \(\int_0^1 \int_x^{e^x} 3xy^2 \, dy \, dx \).4. Compute \(\int_0^1 \int_0^y \int_0^x 6xyz \, dz \, dx \, dy\).5. Compute \(\int_0^1 \int_x^{\pi} \cos(y^2) \, dy \, dx \) 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 \(\int_0^2 \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \frac{xy}{x^2 + y^2} \, dy \, dx \) by converting to polar coordinates.8. Find the \( x \)-coordinate of the center of mass of the lamina that occupies the region \( D = \{(x, y) | 0 \leq x \leq 1, x^2 \leq y \leq 1 \} \) 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^{\ln 4} \int_0^{\ln 3} \int_0^{\ln 2} e^{0.5x

Name: please do question 5 Sure, here's the transcription suitable for an ed
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: please do question 5 Sure, here's the transcription suitable for an educational website:---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 p