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\\[I=\\int_0^{\\var{b1}}\\simplify[std]{e^({a}x)}\\;dx\\]

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

Input your answer to 3 decimal places.

\\[I=\\int_0^{\\var{b2}}\\simplify[std]{1/({b}x+{m2})}\\;dx\\]

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

Input your answer to 3 decimal places.

\\[I=\\int_0^{\\pi/2}\\simplify[std]{({w} * Sin({m3} * x) + {1 -w} * Cos({m3} * x))}\\;dx\\]

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

Input your answer to 3 decimal places.

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Evaluate the following definite integrals.

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Evaluate $\\int_0^{\\,m}e^{ax}\\;dx$, $\\int_0^{p}\\frac{1}{bx+d}\\;dx,\\;\\int_0^{\\pi/2} \\sin(qx) \\;dx$.

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

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b)
\\[\\begin{eqnarray*}I&=&\\int_0^{\\var{b2}}\\simplify[std]{1/({b}*x+{m2})}\\;dx\\\\ &=&\\frac{1}{\\var{b}}\\left[\\ln(\\var{b}x+\\var{m2})\\right]_0^{\\var{b2}}\\\\ &=&\\frac{1}{\\var{b}}\\left\\{ \\ln(\\var{b2*b+m2})-\\ln(\\var{m2})\\right\\}\\\\ &=&\\frac{1}{\\var{b}}\\ln\\left(\\frac{\\var{b2*b+m2}}{\\var{m2}}\\right)\\\\ &=&\\var{ans2}\\mbox{ to 3 decimal places} \\end{eqnarray*} \\]

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