Questions from General Calculus

Q: Show that f∞0e-x2 dx = f10 √-ln

Show that f∞0e-x2 dx = f10 √-ln y, dy by interpreting the integrals as areas.

Q: Find the value of the constant C for which the integral converges

Find the value of the constant C for which the integral converges. Evaluate the integral for this value of C.

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: Find the value of the constant C for which the integral converges

Find the value of the constant C for which the integral converges. Evaluate the integral for this value of C.

Q: Breathing is cyclic and a full respiratory cycle from the beginning of

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about 0.5 L/s. This explains,...

Q: Alabama Instruments Company has set up a production line to manufacture a

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after weeks is (Notice that production approaches 5000 per week...

Q: The velocity graph of a car accelerating from rest to a speed

The velocity graph of a car accelerating from rest to a speed of 120 km/hover a period of 30 seconds is shown. Estimate the distance traveled during this period.

Q: If f is continuous and f40f (x) dx = 10

If f is continuous and f40f (x) dx = 10, find f20f (2x) dx.

Q: If f is continuous and f90 f (x) dx =

If f is continuous and f90 f (x) dx = 4, find f30 xf (x2) dx.

Q: If f is continuous on R, prove that fbaf (-x

If f is continuous on R, prove that fbaf (-x) dx = f-1-bf (x) dx For the case where f (x) > 0 and 0 < a < b, draw a diagram to interpret this equation geometrically as an equality of areas.