Calculus Answers

Evaluate the integral of cos2x dx/(2+5 sin 2x)⁴

Evaluate the integral of √(3x + 1) dx from 1 to 5

Evaluate the integral of (5x+2)³ dx

Evaluate the integral of (3x² - 4 +1) dx

(a) Find the area enclosed by the curve 𝑦 = 25 − 𝑥2

and the straight line 

𝑦 = 𝑥 + 13 correct to 1 decimal place.

(b)Calculate the arc length of the curve 𝑦 = 𝑥

3

2 between 𝑥 = 0 𝑎𝑛𝑑 𝑥 = 1

correct to 1 decimal place

The cost in dollars of producing x headphones is C(x)= 1600+100x-0.1x²

a) calculate average cost of producing 200 headphones

b) calculate the marginal cost of producing the 200th headphone

The number of people attending a music festival is represented by 12000(330-x) where X is the cost of tickets in dollars what ticket price will maximize the total revenue of the concert?

a) what is the optimal ticket price?

b) what will be the total revenue of the festival at that ticket price

A softball diamond has the shape of a square wide sides 60 ft long. If 

a player is running from second base to third at a speed of 24 ft/sec, at 

what rate is his distance from home plate changing when she is 20 ft 

from the third ?

A boy flying a kite pays out string at a rate of 2 ft/sec as the kite moves 

horizontally at an altitude of 100 ft. Assuming there is no sag in the 

string, find the rate at which the kite is moving when 125 ft of string 

have been paid out.

An athlete doing agility training starts at A and runs to point B and then turns and runs back to point A and turns again and runs back to point B. The position for the athlete at time t is given by s(t)=t³-9t-2. On which intervals is the velocity negative? In which direction is the athlete running during these times interval?