Solve $\int_0^1 3xdx$ without using the fundamental theorem of calculus.
I know that, to solve an integral without the fundamental theorem of calculus, I can find the upper sum and the lower sum. I can write down these sums. However, since they have several variables, how do I obtain just one integral value from them?
Best Answer
$\int_0^1 3 x dx$ is the area of the triangle of base $1$ and height $3$. So the answer is $3/2$
This result uses just the property if integrals as the area under the curve.