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How do you integrate by parts?

To integrate the product of two functions - say f(x) = xsinx, the product of g(x) = x and h(x) = sin(x) - the we use integration by parts. Since integration is the inverse of differentiation, we'll appeal to...
PK
Answered by Patrick K. • Maths tutor
6823 Views

Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

First starting from the right hand side. A /(2x + 1) + B /(x + 3) = A(x+3)+B(2x+1)/(x+3)(2x+1) Therefore the numerator = (A+2B)x+(3A+B) Equating this numorator with the Left hand side we are presented with t...
GD
Answered by George D. • Maths tutor
7394 Views

Use the Intermidiate Value Theorem to prove that there is a positive number c such that c^2 = 2.

This exercise is asking to prove the existance of the square root of 2. So let's consider the function f(x) = x^2. Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity). ...
DK
Answered by Dilyana K. • Maths tutor
9678 Views

How do I plot a line on a graph, given the equation y=2x+1 ?

A simple way to do this is to use substitution. You can pick values for x such as x=0,1,2 and find the values for y. When you have two or more coordinates you can plot the line. In this case you could find c...
HP
Answered by Hannah P. • Maths tutor
6460 Views

Given that: y = 5x^3 + 7x + 3. What is dy/dx? What is d^2y/dx^2?

Firslty, the common rule when differentiating is nx m has the derivative of (n)(m)x m-1 . Therefore applying this rule to each individual component of the function: dy/dx=(5)(3)x 3-1 +(7)(1)x 1-1 +(3)(0) =(1...
ME
Answered by Monty E. • Maths tutor
7371 Views