linear differential equation using integrating factor
solve x(dy/dx) + (1+x)y =2  linear equation


solve x(dy/dx) + (1+x)y =2
first divide throughout with x
to make the coefficientof
(dy/dx) as unity

Now identify P = (1/x)+1 , coefficient of y
and Q = 2/x on the R.H.S
use the formula for integrating factor to find the IF
Apply the property of log to change e^(ln x) = x

use the formula for the solution
y(IF) = integral of[Q*IF] dx + C

linear differential equation with integrating


find the mclaurin series for sec x

take y =secx
differentiate to get y' = secxtanx change
secx to y for simpler successive differentiation
continue to differentiate and find the value of y
and the derivatives at x=0 and substitute in
formula for maclaurin series.

maclaurin series for sec x

some problems from integral calculus

* Integrate e^{x^(1/3)}dx

* evaluate integral of [e^(-x) +1] ^2

*evaluate ∫ (sin 3x)^4 dx with limits 0 to pi

* evaluate the integral of sqrt(tan  x)

* evaluate integral of { sqrt{1+(x^2)} } / {x^2}
using integration by parts

*∫ sec³x dx using integration by parts

*integral of (e^(ax) )  cosbx using integration by parts

Area using integral

* evaluate the area of an ellipse (x² /a²) + (y²/b²) =1 using integration

* find the area between y² = x and x² =y

* find the area bounded b y =x² and y = 3x

other questions and problems:

*integral calculus integration formula

trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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