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Evaluate the following definite integral.

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a)
\$I=\\int_1^\\var{b1}\\simplify[std]{({a1} * x ^ 2 + {c1} * x + {d1})^2}\\;dx\$
Expand the parentheses to obtain:

\n

\$\\begin{eqnarray*}I &=& \\int_1^\\var{b1} \\simplify[std]{{a1 ^ 2} * x ^ 4 + {2 * a1 * c1} * x ^ 3+ {c1 ^ 2+2*a1*d1} * x ^ 2 + {2 * c1 * d1} * x+ {d1 ^ 2} }\\;dx\\\\ &=&\\left[\\simplify[std]{{a1 ^ 2}/5 * x ^ 5 + {2 * a1 * c1}/4 * x ^ 4+ {c1 ^ 2+2*a1*d1}/3 * x ^ 3 + {2 * c1 * d1}/2 * x^2+ {d1 ^ 2}x }\\right]_1^\\var{b1}\\\\ &=&\\var{tans1}\\\\ \\\\&=&\\var{ans1}\\mbox{ to 2 decimal places} \\end{eqnarray*} \$

\n

\n

", "variable_groups": [], "name": "Danny's copy of Definite integration 1", "metadata": {"description": "

Evaluate $\\int_1^{\\,m}(ax ^ 2 + b x + c)^2\\;dx$, $\\int_0^{p}\\frac{1}{x+d}\\;dx,\\;\\int_0^\\pi x \\sin(qx) \\;dx$, $\\int_0^{r}x ^ {2}e^{t x}\\;dx$

\n

rebelmaths

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\$I=\\int_1^{\\var{b1}}\\simplify[std]{({a1} * x ^ 2 + {c1} * x + {d1})^2}\\;dx\$

\n

$I=\\;\\;$[[0]]

\n

Input your answer to 2 decimal places.

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