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.