Evaluate the following integrals using trigonometric
identities
(a) intergal sin6 x cos3 x dx
(b) Z...
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
(15) Evaluate each of the following integrals. (a) Z cos(x)
ln(sin(x)) dx (b) Z x arcsin(x 2 ) dx (c) Z 1 0 ln(1 + x 2 ) dx (d)
Z 1/4 0 arcsin(2x) dx
(16) Use the table of integrals to evaluate the integrals, if
needed. You may need to transform the integrand first.
(a) Z cos(4t) cos(5t)dt
(b) Z 1 cos3 (x) dx
(c) Z 1 x 2 + 6x + 9 dx
(d) Z 1 50 −...
Solve the following integrals using integration by parts
technique:
a) [int] xsinx dx
b) [int] x^2sinx dx
c) [int] xcosx dx
d) [int] sin(sqrt(x)) dx
e) [int] xexp(x) dx
f) [int] x / exp(x) dx
1) Find the following indefinite integrals.
a) (4-3xsec^2 x)/x dx
b) (5 sin^ 3 x ) / (1+cosx)(1-cosx) dx
2) A particle starts from rest and moves along the x-axis from
the origin at t = 0 with acceleration
a(t) = 6 - 2t
(ms^-2) at time t. When and where will it come to rest.
Remember dvdt =
acceleration and dsdt = velocity
3) Use substitution to find the following integrals.
a) (9x)/ sqrt...
Evaluate the following integral using trigonometric
substitution. a) find the partial decomposition of the integrand b)
evaluate the indefinite integral
1. 6/x(x^2+2)^2
2. 5/x(x^2+1)^2?
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