Definite integrals.

**zdawg** · January 3rd, 2011, 06:52 PM

i need help with these problems please?:

(bSa is the intergration symbol with the a and b values)

1S0 36dx/(2x+1)^3

(pi)/2S0 5sin^(3/2)xcosxdx

(pi)/4S0 e^(tanx)sec^2xdx

**pickslides** · January 3rd, 2011, 07:02 PM

Originally Posted by zdawg

1S0 36dx/(2x+1)^3

Just clarifying $\displaystyle\int_0^1 \frac{36}{(2x+1)^3}~dx$ ?, if so use a substitution $\displaystyle u= 2x+1$

**zdawg** · January 3rd, 2011, 07:03 PM

yeah, thats what i ment, sorry.

**pickslides** · January 3rd, 2011, 07:07 PM

Well as I pointed out $\displaystyle\int_0^1 \frac{36}{(2x+1)^3}~dx$

Make $\displaystyle u= 2x+1\implies \frac{du}{dx} = 2$

Giving $\displaystyle\int_0^1 \frac{2\times 18}{(2x+1)^3}~dx = \int_1^3 \frac{ 18}{(u)^3}~du= 18\int_1^3 \frac{ du}{(u)^3}$

**zdawg** · January 3rd, 2011, 07:11 PM

my txtbk says the final answer is 8, do you know how to get there?

**pickslides** · January 3rd, 2011, 07:18 PM

Originally Posted by zdawg

my txtbk says the final answer is 8, do you know how to get there?

I do, by completeing the hints given in post #4. Can you finish it using simple integration?

**mr fantastic** · January 3rd, 2011, 08:57 PM

Originally Posted by zdawg

[snip]

(pi)/2S0 5sin^(3/2)xcosxdx

(pi)/4S0 e^(tanx)sec^2xdx

(b) Substitute $u = \sin (x)$ .

(c) Substitute $u = \tan (x)$ .

If you need more help, post what you can do and make it clear where you get stuck.

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