1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx)
(a) What is the first step of your ‘new’ integral?
(b) What is the final antiderivative step before evaluating?
(c) What is the answer in simplified exact form?
2) indefinite integral (cos^2 2theta) / (cos^2 theta) dtheta
(a) What is the first step of your ‘new’ integral?
(b) What is the simplified integral before taking the
antiderivative?
(c) What is the answer in simplified form?
Evaluate the integral: ∫√36x^2−49 / x^3 dx
(A) Which trig substitution is correct for this integral?
x=49/36sec(θ)
x=7/6sec(θ)
x=1/36sec(θ)
x=6/7sec(θ)
x=7/6sin(θ)
(B) Which integral do you obtain after substituting for
xx?
Note: to enter θθ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?
Note: WAMAP does not recognize the inverse secant (arcsec)
function. You will need to...
a, evaluate the definite integral: 2 to 3 x2/square
root of x3-7 dx
b, Determine the indefnite integral :
12x5-5x/x2 dx
c, Evaluate the integral : 10x sin (2x+3) dx
d, Evaluate the integral: 1/x2 square root of
36-x2 dx
A. Find the indefinite integral.
B. Find the indefinite integral.
C. Find the derivative.
f(x) = x6 ·
log3(x)
Give your answer using the form below.
xA(B + C
logD(x))
A =
B =
C =
D =
D. Find the indefinite integral.
E. Find the area under the curve below from x = 1 to
x = 2. Give your answer correct to 3 decimal places.
F. Find the area under the curve below from x = 0 to...
Evaluate each integral using trig substitutions
1.) Integral of (3x^5dx)/(sqrt(16-x^2)
2.) Integral of (sqrt(x^2-16)dx)/x
3.) Integral of (6dx)/(16+16x^2)
Evaluate the integral: ∫−14 / x^2√x^2+100 dx
(A) Which trig substitution is correct for this integral?
x=−14sec(θ)
x=100sec(θ)
x=10tan(θ)
x=100sin(θ)
x=10sin(θ)
x=100tan(θ)
(B) Which integral do you obtain after substituting for x and
simplifying?
Note: to enter θ, type the word theta.
(C) What is the value of the above integral in terms of θ?
(D) What is the value of the original integral in terms of x?