Definite Integral

Problem : Given that e ^x dx = e ² - and e ^x dx = 1 - , find e ^x dx .

Solution for Problem 1 >>

By telescoping limits, we have

e x dx + e x dx = e x dx

so

e x dx = e 2 - - 1 - = e 2 - 1.

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

Solution for Problem 2 >>

Here we use all three properties introduced in this section:

x 2 + 2xdx	=	x 2 dx + 2 xdx + x 2 + 2xdx
	=	+2 +
	=

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Problem : Compute + 3 dx using elementary geometry.

Solution for Problem 3 >>

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 .

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