Question

Find the area under the curve y=x^2 + 1 and the x-axis between x=0 and x=3. *

Answer 1

$\mathrm{The\:area\:under\:a\:curve\:is\:the\:area\:between\:a\:curve}\:f\left(x\right)\:\mathrm{and\:the\:x-axis\:on\:an\:interval}\:\left[a,\:b\right]\:\mathrm{given\:by}\\ A=\int _a^b|f\left(x\right)|dx\\ =\int _0^3\left|x^2+1\right|dx\\ =12$