If A, B, C are three non- collinear points with position vectors respectively, then show that the length of the perpendicular from C on AB is
Draw a rough sketch of the curve and find the area of the region bounded by curve y2 = 8x and the line x =2.
Sketch the graph of y = |x + 4|. Using integration, find the area of the region bounded by the curve y = |x + 4| and x = – 6 and x = 0.
Given, y = |x + 4|
y = (x + 4), if x > 4 & y = - (x + 4), if x < 4
For y = x + 4 For y = - x - 4
when x = 0, y = 4 when x = 0, y = - 4
& when y = 0, x = - 4 when y = 0, x = - 4
Points are (0, 4) and (- 4, 0) Points are (0, - 4) and (-4, 0)
Required area =
=
=
=
=
= - 2 + 8
= 10 sq. units
Thus, the area of the region is 10 sq. units.