Graphics Programs Reference
In-Depth Information
ans =
2*x/(1+(x^2+1)^2)
Problem 3
We compute the following integrals.
(a)
int(cos(x), x, 0, pi/2)
ans =
1
(b)
int(x*sin(xˆ2), x)
ans =
-1/2*cos(x^2)
To check the indefinite integral, we just differentiate.
diff(-cos(xˆ2)/2, x)
ans =
x*sin(x^2)
(c)
int(sin(3*x)*sqrt(1 - cos(3*x)), x)
ans =
2/9*(1-cos(3*x))^(3/2)
diff(ans, x)
ans =
sin(3*x)*(1-cos(3*x))^(1/2)
(d)
int(xˆ2*sqrt(x + 4), x)
ans =
2/7*(x+4)^(7/2)-16/5*(x+4)^(5/2)+32/3*(x+4)^(3/2)
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