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)
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...
Evaluate the following integral ∫ ∫ R 4x + y (3x − y) ln(3x − y)
dA where R is the region bounded by the graphs of y = 3x − e7,
y = 3x − e5, y = −4x + 8, and y = −4x + 5. Use the change
of variables u = 3x − y, v = 4x + y.