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. What is the difference between the Riemann integral and the
Darboux Integral?
2. Give the same characteristics between Riemann integrals and
Darboux integrals !.
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?
evaluate the integral by making an appropriate change of
variables
double integral of 5sin(25x^2+64y^2) dA, where R is the region
in the first quadrant bounded by the ellipse 25x^2 +64y^2=1
1) what are Cauchy’s Integral Theorem and Cauchy's integral
formula
2) Explain about the consequences and applications of these
theorems.
3) Explain about different types of singularities and the
difference between Taylor series and Laurent series.
Evaluate the integral Integral from 1 divided by 2 to 1 left
parenthesis x Superscript negative 3 Baseline minus 15 right
parenthesis dx using the Fundamental Theorem of Calculus.
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.
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...