How do you integrate xln(x) between the limits of 0 and 2?
In order to answer this question you need to use integration by parts.Using the standard integration by parts formula: ∫u dv/dx dx = uv-∫v du/dx dx.Let:u=ln(x) v=(1/2)x2du/dx=1/x dv/dx=xTherefore we get:I=[1/2xln(x)-1/2∫xdx]20We now know how to integrate x. It becomes 1/2x2. Therefore the overall integral becomes:I=[1/2xln(x)]20-[1/4x2]20I=2ln(2)-1I=ln(4/e)I ≈ 0.386
LK
Related Maths IB answers
All answers ▸What is a geometric sequence?
In an arithmetic sequence, the first term is 2, and the fourth term is 14. a) Find the common difference, d. b) Calculate the sum of the first 14 terms, S14.
The sum of the first n terms of an arithmetic sequence is Sn=3n^2 - 2n. How can you find the formula for the nth term un in terms of n?
A scalene triangle has base of 5cm. The angle opposite to the base is 63°, and a second angle is 72°. Find the area of the traingle