Lmao those integrals are the same so it’s true for all real numbers, they’re both 4x + 6x^(2/3) if you just rewrite the radical on the left, no calculus involved because if two things are equal to each other then the equation is true for all real numbers
You could’ve given a better example. That integration problem is an easy polynomial with the power rule and you don’t have to deal with any advanced integration techniques.
The left and right sides are already balanced, all you really need to know is your rules of exponents and just rewrite the equations the same then derivate if needed
Top one is simple power rule, add 1 to the power of x and then multiply the coefficient by the reciprocal of the resulting exponent. Then just F(b) - F(a) and you’re done
Hey, if you don't know anything about the top equation, or even if you think you know everything about calculus, I would highly recommend checking out 3blue1brown on YouTube and watching his Essence of Calculus series. It's high quality stuff, and the concepts are explained intuitively and visually.
... it’s not some fancy equation where you need to find x, just evaluate the integral from 0 to 1. Doesn’t even have transcendental functions or fractions, shit it’s literally just power rule
Putting x to the 2/3 power is the same thing as squaring x and then taking the cube root. The top equation isn’t even a problem, it’s just showing the two expressions are equal
Okay but the first part isnt even a question. Its just showing that roots are just fractional powers. It has nothing to do with the integral. Its already a completed statement
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