Calculus Answers

Integrate dx/(25x²-4)½ using trigonometric substitution

FIND THE MAXIMUM AND THE MINIMUM VALUES OF
3X^4 - 2X^3 - 6X^2 + 6X + 1 IN THE INTERVAL [0,2] IF THEY EXIST

Integrate dx/(25x²-4)½

Integrate x²dx/(9-x²)½

Integrate dx/(4+2²)½ dx

Integrate sin³x dx

Integrate tan³x dx

A straight train track running north-south on a flat and otherwise featureless plain meets a straight road running east-west at right angles. As the last car of a train heading north at 100 km/h passes this intersection, a drone is flying west directly over the road at 200 km/h is 1 km east of the intersection. At this instant, the drones controller decides to have it chase the train and thereafter keeps the drone headed directly towards the last car of the train until it catches up. If the train and drone maintain their speeds of 100 km/h and 200 km/h, how far from the crossing does the drone catch up with the last car of the train?

Expand the function
f(x)=x^4-1 in a series of the form

(infinity)sum(k=0)=AkPk(x)

Using Rodrigue’s formula, obtain expression for the Hermite polynomial
H3(x)
and show that
H3'(x) = 6H2(x)