What is the area of the region in the first quadrant?

Question

Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the curve  y= 1/sqrt(x) and the x-axis.

Answer 1

First find the points where y = 1/√x intersects the line y= 8x and the line x=1

A= ∫^1/4₀8x dx + ∫¹_1/4 [1 / √x ] dx

=[ 4x² ] |₀^1/4 + [ 2√x] |¹_1/4

= 1/4 +2 -1

=5/4