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Question

Mathematics Question on integral

Evaluate the definite integral: ∫231xdx∫^3_2 \frac{1}{x}dx

Answer

The correct answer is: =log∣3∣−log∣2∣=log32=log|3|-log|2|=log\frac{3}{2}
Let I=∫231xdxI=∫^3_2 \frac{1}{x}dx
∫1xdx=log∣x∣=F(x)∫\frac{1}{x}dx=log|x|=F(x)
By second fundamental theorem of calculus,we obtain
I=F(3)−F(2)I=F(3)-F(2)
=log∣3∣−log∣2∣=log32=log|3|-log|2|=log\frac{3}{2}