Integrate xcos(x) with respect to x
Using LATEX (Logarithms, Algebra, Trigonometry, Exponential and Complex numbers) to determine which variable is du and which is dv/dx. This is decided by using the above acronym. For example in this question 'x' is an algebraic variable and 'cos(x)' is a trigonometric variable, hence 'x' is du and cos(x) is dv/dx. To solve this question, we use integration by parts and use the following formula. du.dv- integral(dv.(du/dx)dx).
du = x hence du/dx = 1 (differentiate du) dv/dx = cosx hence dv = sinx (integrate dv/dx)
Plug in the values in the above equation.
Ans = xsinx + cosx + c
VP
Answered by Vishnu P. • Further Mathematics tutor
3212 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸For a homogeneous second order differential equation, why does a complex conjugate pair solution (m+in and m-in) to the auxiliary equation result in the complementary function y(x)=e^(mx)(Acos(nx)+Bisin(nx)), where i represents √(-1).
Sketch the locus of z on an Argand diagram if arg[(z-5)/(z-3)] = π/6
What are imaginary numbers and why do we use them?
Integrate the function f(x) = x ln (x) over the interval [1,e].