To find the area of the curve subject to these constraints, we must take the integral of y = x ^ (1/2) + 2 from x=1 to x=4 Take the antiderivative: Remember that this what the original function would be if our derivative was x^(1/2) + 2 antiderivative (x ^(1/2) + 2) = (2/3) x^(3/2) + 2x * To check that this is correct, take the derivative of our anti-derivative and make sure it equals x^(1/2) + 2
To find integral from 1 to 4: Find anti-derivative at x=4, and subtract from the anti-derivative at x=1 2/3 * 4 ^ (3/2) + 2(4) - (2/3) *1 - 2*1 2/3 (8) + 8 - 2/3 - 2 Collect like terms 2/3 (7) + 6 Express 6 in terms of 2/3 2/3 (7) + 2/3 (9) 2/3 (16) = 32/3 = 10 2/3 Answer is B
It is split into 8 equal parts, if you want to see how likely you're going to get red, look at how many red parts there are. 2. Now make it into a fraction! 2/8, but we need it to be simplified so it is 1/4.
