Business Calculus
Evaluate the integral: ∫xsinxdx{{\(\displaystyle\]\int\) x\(\sin\) x\,dx}}
Evaluate ∫x2cosxdx \(\int\) x^2 \(\cos\) x \, dx using integration by parts.
Evaluate the limit by interpreting it as a Riemann sum and then computing the corresponding integral.
limn→∞∑k=1n1nln(1+2kn) \(\displaystyle\) \(\lim\)_{n\(\to\[\infty\)}\(\sum\)_{k=1}^n\(\frac{1}{n}\]\ln\[\left\)(1+\(\frac{2k}{n}\]\right\))
Evaluate the improper integral ∫5∞dxx2 \(\int\)_5^{\(\infty\)} \(\frac{dx}{x^2}\) .
Evaluate the improper integral ∫091x+3xdx \(\int\)_{0}^{9} \(\frac{1}{x + 3\sqrt{x}\)} \, dx .
Complete the square to evaluate ∫−∞∞e−(2x2−3x+1)dx\(\int\)_{-\(\infty\)}^{\(\infty\)}e^{-(2x^2-3x+1)}\,dx given the Gaussian integral formula ∫−∞∞e−ax2dx=πa\(\int\)_{-\(\infty\)}^{\(\infty\)}e^{-ax^2}dx=\(\sqrt{\frac{\pi}{a}\)}.
