Evaluate the integral. (Use C for the constant of
integration.)
(x^2-1)/(sqrt(25+x^2)*dx
Evaluate the integral. (Use C for the constant of
integration.)
dx/sqrt(9x^2-16)^3
Evaluate the integral. (Use C for the constant of
integration.)
3/(x(x+2)(3x-1))*dx
question 1
Distinguish between a definite integral and an indefinite
integral. (use
examples)
question 2
What is the conceptual meaning of the derivative? State an
example.
question 3
Find the area of the region bounded by y = 9 - x^2 and y = 0.
Sketch the
graph and shade the region. Graph on attached grid paper. Make sure
the
graphs are accurate and not just rough sketches.
1.) Evaluate the given definite integral.
Integral from 4 to 5 dA∫45 (0.2e^−0.2A +3/A) dA
2.) Evaluate the definite integral.
Integral from negative 1 to 1 dx∫−1 1 (x^2+1) dx
3.) Evaluate the definite integral.
Integral from 0 to 2 dx∫02 (2x^2+x+6) dx
4.) Evaluate the definite integral.
Integral from 1 to 4 left dx∫14 (x^3/2+x^1/2−x^−1/2) dx
5.) Evaluate the definite integral.
Integral from negative 2 to negative 1 dx∫−2−1 (3x^−4) dx
Evaluate the double integral explicitly by reversing the order
of integration:? Integral from 0 to 8 and integral from (sub3
square root of y) to 2 ex dxdy
Instructions: For each solid described, set up, BUT DO
NOT EVALUATE, a single definite integral that represents the exact
volume of the solid. You must give explicit functions as your
integrands, and specify limits in each case. You do not need to
evaluate the resulting integral.
1. The solid generated by rotating the region enclosed by the
curves y = x^2 and y = x about the line x-axis.
1. use the shell method to write and evaluate the definite
internal that represents the volume of the solid generated by
revolving the plan region about the x-axis. x+y^2=4
2. use the shell method find the volume of the solid generated
by revolving the region bounded by the graphs of the equations
about the given line. y=(x)^1/2. y=0 x=4. about the line x=6
Use Simpson’s Rule with n = 4 to approximate the value of the
definite integral ∫4 0 e^(−x^2) dx. (upper is 4, lower is 0)
Compute the following integrals (you may need to use Integration
by Substitution):
(a) ∫ 1 −1 (2xe^x^2) dx (upper is 1, lower is -1)
(b) ∫ (((x^2) − 1)((x^3) − 3x)^4)dx