Calculus Answers

find the total length of the curve r=4(1-sin theta) form theta = 90 degree to theta= 270 degree

compute the surface area generated when the first quadrant portion of the curve x^2-4y=8 from x1=0 to x2= 2 is revolved about the y-axis

2. ∫ 12𝑥² √4𝑥³ + 7𝑑𝑥

∫ (𝑥2²+ 5)³2𝑥𝑑𝑥

1. ∫ (𝑥²+5)³ 2𝑥𝑑𝑥

2. ∫ 12𝑥² √4𝑥³ + 7𝑑𝑥

3. ∫ √2𝑥³+7 𝑥²𝑑𝑥

4. ∫ 5𝑥√1 + 4𝑥²

5. ∫(3𝑥² − 4𝑥 + 2)² (3𝑥 − 2)𝑑𝑥

Find the volume of the solid by revolving the astroid x⅔+y⅔=a⅔ along x axis

Find the perimeter of loop of the curve 3ay²=x²(a-x)

Find the derivatives of each of the following functions:

a. 𝑦 = 5𝑥²+7𝑥−8

b. 𝑓(𝑥) = 7/𝑥⁴

c. 𝑦 = 15/√𝑥

d. 𝑓(𝑥) = 2𝑥^7/2−𝑥^-1/3

e. 𝑦 = (4𝑥²−7𝑥)/𝑥

f. 𝑓(𝑥) = 7𝑥³/√𝑥

Differentiate with respect to 𝑥

a. (7𝑥 – 4 )³

b. √(6𝑥+4)

The curve 𝑦=−𝑥³+3𝑥²+6𝑥−8 cuts the 𝑥-axis at 𝑥=−2,𝑥=1 and 𝑥=4.

a. Sketch the curve, showing clearly the intersection with the coordinate axes.

b. Differentiate 𝑦=−𝑥³+3𝑥²+6𝑥−8

c. Show that the tangents to the curve at 𝑥=−2 and 𝑥=4 are parallel.