Question

3. Determine $\int 2x^2(3x^3 + 2)^7 dx$ 4. Evaluate $\int_0^{\pi/2} 2\sin^3 x \cos^2 x$. Show your working 5. Evaluate $\int_0^1 2e^{5x} \cos 2x dx$ 6. The area enclosed between the x-axis, the curve x(4 - x) and the ordinates x = 2 and x = 4 is rotated through $2\pi$ radians about the x axis. Calculate: 1. Length of the arc from x = 2 and x = 4 2. The rotating area and the coordinates of its centroid: 3. The volume of the solid of revolution formed and the coordinates of its centre of gravity

          3. Determine $\int 2x^2(3x^3 + 2)^7 dx$
4. Evaluate $\int_0^{\pi/2} 2\sin^3 x \cos^2 x$. Show your working
5. Evaluate $\int_0^1 2e^{5x} \cos 2x dx$
6. The area enclosed between the x-axis, the curve x(4 - x) and the ordinates x = 2 and x = 4 is rotated through $2\pi$ radians about the x axis. Calculate:
1. Length of the arc from x = 2 and x = 4
2. The rotating area and the coordinates of its centroid:
3. The volume of the solid of revolution formed and the coordinates of its centre of gravity

3. Determine ∫ 2x^2(3x^3 + 2)^7 dx
4. Evaluate ∫0^π/2 2sin^3 x cos^2 x. Show your working
5. Evaluate ∫0^1 2e^5xcos 2x dx
6. The area enclosed between the x-axis, the curve x(4 - x) and the ordinates x = 2 and x = 4 is rotated through 2π radians about the x axis. Calculate:
1. Length of the arc from x = 2 and x = 4
2. The rotating area and the coordinates of its centroid:
3. The volume of the solid of revolution formed and the coordinates of its centre of gravity

Added by Lisa T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

05/17/2023

Step 1

Step 1: To determine 2x^2 + 3x + 2dx, we can simply integrate each term separately. Show more…

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Texts: question 6 3. Determine 2x^2 + 3x + 2dx. 4. Evaluate ∫(22sin^3x cosx)dx. Show your working. 5. Evaluate ∫(2e^5x cos2x)dx. 6. The area enclosed between the x-axis, the curve x^4 - x, and the ordinates x = 2 and x = 4 is rotated through 2π radians about the x-axis. Calculate: 1. The length of the arc from x = 2 and x = 4. 2. The rotating area and the coordinates of its centroid. 3. The volume of the solid of revolution formed and the coordinates of its center of gravity.