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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) = 2𝑥7/2−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.