Questions from General Calculus

Q: Use Simpson’s Rule with n = 6 to estimate the area under

Use Simpson’s Rule with n = 6 to estimate the area under the curve y = ex/x from x = 1 to x = 4.

Q: Find the most general antiderivative of the function. /

Find the most general antiderivative of the function.

Q: Find the most general antiderivative of the function. /

Find the most general antiderivative of the function.

Q: Use Property 8 of integrals to estimate the value of f31√

Use Property 8 of integrals to estimate the value of f31√x2 + 3, dx.

Q: Use the properties of integrals to verify that 0 < f10x4 cos

Use the properties of integrals to verify that 0 < f10x4 cos x dx < 0.2.

Q: Use Newton’s method to find the coordinates, correct to six decimal

Use Newton’s method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x – 1)2 that is closest to the origin.

Q: Evaluate the integral or show that it is divergent. f

Evaluate the integral or show that it is divergent. f∞11/ (2x + 1)3, dx

Q: Use a graph to give a rough estimate of the area of

Use a graph to give a rough estimate of the area of the region that lies beneath the given curve. Then find the exact area.

Q: Evaluate the integral or show that it is divergent. f

Evaluate the integral or show that it is divergent. f∞0ln x/x4, dx

Q: Evaluate the integral or show that it is divergent. f0

Evaluate the integral or show that it is divergent. f0-∞e-2x dx