Questions from General Calculus

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Q: Sketch the region bounded by the curves, and visually estimate the

Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.

Q: Sketch the region bounded by the curves, and visually estimate the

Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.

Q: Sketch the region bounded by the curves, and visually estimate the

Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordinates of the centroid.

Q: Calculate the moments Mx and My and the center of mass of

Calculate the moments Mx and My and the center of mass of a lamina with the given density and shape.

Q: Calculate the moments Mx and My and the center of mass of

Calculate the moments Mx and My and the center of mass of a lamina with the given density and shape.

Q: A hole of radius is bored through the middle of a cylinder

A hole of radius is bored through the middle of a cylinder of radius R > r at right angles to the axis of the cylinder. Set up, but do not evaluate, an integral for the volume cut out.

Q: Evaluate the definite integral. fa0 x√a2 – x2

Evaluate the definite integral. fa0 x√a2 – x2, dx

Q: (a). Show that f∞-∞ x dx is divergent.

(a). Show that f∞-∞ x dx is divergent. (b). Show that This shows that we can’t define

Q: If f∞-∞ f (x) dx is convergent and a

If f∞-∞ f (x) dx is convergent and a and b are real numbers, show that