Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found
Using integration by parts, we can re-write the integral of ln(x) as (xln(x) - int(x(1/x))) = x*ln(x) - x
Therefore, evaluating between 2 and 4 gives us (4ln(4) - 4) - (2ln(2) - 2) = 2ln(16/2) - 4 + 2 = ln(64) - 2. So a = 64 and b = 2
KR
Related Maths A Level answers
All answers ▸You have a five-litres jug, a three-litres jug, and unlimited supply of water. How would you come up with exactly four litres of water (with no measuring cup)?
A Polynomial is defined as X^3-6X^2+11X-6. a)i Use the factor theorem to show that X-3 is a factor. ii Express as a linear and quadratic b)Find the first and second derivative c) Prove there is a maximum at y=0.385 to 3DP
Differentiate the function y = 26 + x - 4x³ -½x^(-4)
Solve the equation 3x^2/3 + x^1/3 − 2 = 0