Definite Integral

Topics

Definite Integral Problems 2

Save

Topics Definite Integral Problems 2

Problem : Given that e^xdx = e² - and e^xdx = 1 - , find e^xdx.

By telescoping limits, we have

e^xdx +

e^xdx =

e^xdx

so

e^xdx =

e² -

-

1 -

= e² - 1.

Problem : If xdx = 3/2, x²dx = 7/3, and (x² + 2x)dx = 180/3, find (x² + 2x)dx.

Here we use all three properties introduced in this section:

x² + 2xdx	=	x²dx + 2xdx + x² + 2xdx
	=	+2 +
	=

Problem : Compute + 3dx using elementary geometry.

We have

+ 3dx	=	dx + 3dx
	=	+ 6

since the two integrals correspond respectively to a semicircle of radius 1 and a rectangle with height 3 and width 2.

Previous section Next section

Take a Study Break