Questions from General Calculus

Q: Evaluate the integral or show that it is divergent. f101

Evaluate the integral or show that it is divergent. f101/2 – 3x, dx

Q: Evaluate the integral or show that it is divergent. fe1dx

Evaluate the integral or show that it is divergent. fe1dx/x √lnx

Q: Find the volume of the solid obtained by rotating about the x

Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curves y = e-2x, y = 1 + x and x = 1.

Q: Evaluate the integral or show that it is divergent. f62y

Evaluate the integral or show that it is divergent. f62y/√y – 2, dy

Q: Use the Comparison Theorem to determine whether the Integral is convergent or

Use the Comparison Theorem to determine whether the Integral is convergent or divergent.

Q: For what values of a is f∞0eax cos x dx

For what values of a is f∞0eax cos x dx convergent? Use the Table of Integrals to evaluate the integral for those values of a.

Q: A particle moves along a line with velocity function v (t

A particle moves along a line with velocity function v (t) = t2 - t, where is measured in meters per second. Find (a) the displacement and (b) the distance traveled by the particle during the time int...

Q: (a). Evaluate the integral f∞0 xne-x

(a). Evaluate the integral f∞0 xne-x dx for n = 0, 1, 2, and 3. (b). Guess the value of f∞0 xne-x dx when n is an arbitrary positive integer. (c). Prove your guess using mathematical induction.

Q: Evaluate the integral. f01 x4/5 dx

Evaluate the integral. f01 x4/5 dx

Q: The speedometer reading (v) on a car was observed at

The speedometer reading (v) on a car was observed at 1-minute intervals and recorded in the chart. Use Simpson’s Rule to estimate the distance traveled by the car.