Iterated Integral Homework: Evaluate I=∫01∫1+y1-y(6y2+10x)dxdy

[shards5]

Homework Statement

Evaluate the iterated integral I = $$\int^{1}_{0}\int^{1+y}_{1-y} (6y^2+ 10x) dxdy$$

Homework Equations

. . . ?

The Attempt at a Solution

Integrate with respect to x gives me the following equation.
$$\int^{1}_{0} 6xy^2 + 5x^2 dy$$
I plug in y+1 and y-1 into x and get the following
6y²+12y³+6y⁴+5+10y+5y²-6y+12y³-6y⁴-5+10y-5y²
Most of the stuff cancels out giving me
12y³+12y³+10y+10y
which simplifies to
$$\int^{1}_{0} 24y^3+20y dy$$
and after integration I get
6y⁴+10y²
and after plugging in my numbers I get
6+10 = 16 which is wrong. I am not sure where I screwed up.

 

[jhae2.718]

Don't use sup in LaTeX; exponents are indicated by ^, with braces {} if the exponent is more than one character long.

I only briefly looked at your work, but you might want to check your substitution of limits in the first integrand.

 

[jhae2.718]

<double post>

 

[shards5]

You, were right! I screwed up by substituting the limits into the y instead of x by mistake. Thanks a lot.