Just these 2 questions if anyone can lend a hand
1.Find the minimum area of the part bounded by the parabola and the line .
2. Evaluate
First time on this forum, any help will be greatly appreciated!!! XD
Just these 2 questions if anyone can lend a hand
1.Find the minimum area of the part bounded by the parabola and the line .
2. Evaluate
First time on this forum, any help will be greatly appreciated!!! XD
you want to minimize the area, so this is an optimization problem. those are all done the same way, so you should have an idea of how to proceed.
the area will be given by an integral, first set this up. find the limits and then set up the integral for (top function) - (bottom function) over those limits. you want to minimize the resulting intral. note that you may not have to do the integral, though it is simple enough to do if you choose. you can apply the second fundamental theorem of calculus to find the derivative of the function defined as the integral
substitution works here. first note that you can write the integral as by multiplying by . Now, let and continue via integration by substitution.2. Evaluate
Welcome! ...you meant to say "help" as opposed to "thanks" right?First time on this forum, any thanks will be greatly appreciated!!! XD
I must admit, the second problem is more complicated than i realized (where's Krizalid when you need him?!) my substitution was a knee-jerk reaction . there is no primitive integral here, but with the limits, things work out (Maple gave an answer of ln(2)), so we have to employ some trick. i am thinking about using double integrals. have you done those?