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Evaluate the ∫(z+2)/(z²+4z) dz from -3 to 2
Find the volume of the solid inside the surface r
2 + z
2 = 4 and outside the surface r = 2 cos θ.
Trace the
curve
x^2 y^3 =9(y^2-x^2)
If 𝑎 = 4𝑡^(− 3/2) , 𝑠 = 16 𝑤ℎ𝑒𝑛 𝑡 = 4, 𝑎𝑛𝑑 𝑠 = 25 𝑤ℎ𝑒𝑛 𝑡 = 6, find the equation of motion 𝑠 = 𝑓(𝑡) and the velocity function 𝑣(𝑡).
The points (-1,3) and (0,2) are on a curve, and at any point (x,y) on the curve (𝑑^2𝑦) /(𝑑𝑥^2) = 2 − 4𝑥. Find an equation of the curve.
The points (-1,3) and (0,2) are on a curve, and at any point (x,y) on the curve 𝑑 2𝑦 𝑑𝑥 2 = 2 − 4𝑥. Find an equation of the curve.
6) Find the Antiderivative of sec(x) tan(x)dx- if you found an antiderivative for this explain why the result for the definite integral using the same function is undefined??
7) Given the function h(x)= (square root of x)*ln(sin(x))--> Use a calculator to evaluate each of the following and round to the nearest thousandth (3 decimal places).
**Given--> h(x)= (square root of x)*ln(sin(x))
a) The integral from 0.5 to 3 h(x)dx
b)The integral from 3 to 2 h(x)dx
c)The integral from 7 to 9 |h(x)| dx
1) Antiderivative of -4csc(x)cot(x)dx :Show all work
2) Antiderivative of -1cot^2(x)dx :Show all work
3) Antiderivative of ((6/x^3)+cube root of x^2)dx :Show all work
4) Write the Antiderivative and definite integral (leave in terms of e if applicable) --> the integral from -1 to 3 (10e^x-4x)dx
5) Write the Antiderivative and definite integral(leave in radical form if applicable)--> the integral from (pi/2) to (5pi/6) (-3cos(x)-4sin(x))dx
1) Antiderivative of -4csc(x)cot(x)dx :Show all work
2) Antiderivative of -1cot^2(x)dx :Show all work
3) Antiderivative of ((6/x^3)+cube root of x^2)dx :Show all work
4) Write the Antiderivative and definite integral (leave in terms of e if applicable) --> the integral from -1 to 3 (10e^x-4x)dx
5) Write the Antiderivative and definite integral(leave in radical form if applicable)--> the integral from (pi/2) to (5pi/6) (-3cos(x)-4sin(x))dx
6) Find the Antiderivative of sec(x) tan(x)dx- if you found an antiderivative for this explain why the result for the definite integral using the same function is undefined??
7) Given the function h(x)= (square root of x)*ln(sin(x))--> Use a calculator to evaluate each of the following and round to the nearest thousandth (3 decimal places).
**Given--> h(x)= (square root of x)*ln(sin(x))
a) The integral from 0.5 to 3 h(x)dx
b)The integral from 3 to 2 h(x)dx
c)The integral from 7 to 9 |h(x)| dx
A function f(x) is strictly decreasing on the interval [a,b].Would a Right Riemann Sum overestimate or underestimate the definite integral from a to b f(x)dx? Explain your answer!
