Evaluate the following integral using trigonometric
substitution. a) find the partial decomposition of the integrand b)...
Evaluate the following integral using trigonometric
substitution. a) find the partial decomposition of the integrand b)
evaluate the indefinite integral
Evaluate the following integrals using trigonometric
identities
(a) intergal sin6 x cos3 x dx
(b) Z π/2
o
cos5 x dx
(c) Z
sin3
(
√
x)
√
x
dx
(d) Z
tsin2
t dt
(e) Z
tan2
θ sec4
θ dθ
(f) Z
x sec x tan x dx
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...
For each of the following integrals find an appropriate
trigonometric substitution of the form x=f(t)x=f(t) to simplify the
integral.
the inteagral
a) ∫x(3x^2+30x+73)^(1/2)dx
b)∫x/(−25−3x^2+18x)^(1/2)dx
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?
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...
Draw the region and evaluate the following integral(a) ∫10∫21(y+2x)dydx∫01∫12(y+2x)dydx (b) ∫10∫xx2xydydx∫01∫x2xxydydx (c) ∫π0∫πysinxxdxdy∫0π∫yπsinxxdxdy
Partial Fractions: Problem 2
Use the method of partial fraction decomposition to write the
following rational expression as the sum of simpler rational
functions whose denominators are polynomials of degree 1.
−20x+20/x^2−x−56=