hello, can someone help me these questions?
a) {{{ int ( lnt/sqrt(t), dt, 4, 9) }}}
b) {{{ int ( cos(sqrt(6x)), dx ) }}}
One way of stating the formula for integration by parts is:
$\displaystyle \displaystyle \int_a^b f'(x)g(x)\;{dx} = g(x)\cdot f(x)\bigg|_{a}^{b}-\int_a^b f(x)g'(x)\;{dx} $
Therefore (without defining new variables) we can write the integral as:
$\displaystyle \displaystyle \int_4^9 \frac{\ln{t}}{\sqrt{t}}\;{dt} = 2\int_4^9 (\sqrt{t})'\ln{t}}\;{dt} = 2\sqrt{t}\ln{t}\bigg|_4^9-2\int (\ln{t})'\sqrt{t}\;{dt} $