Hello! I have a quick question that confused me for some time.
I have this question:
Determine[MATH]\frac{d}{dx}\int\limits_{x^2}^0 \frac{1}{t^4+1}dt[/MATH]
My first idea was to solve it through this method:
1. [MATH]=\frac{d}{dx}\int\limits_0^{x^2} \frac{-1}{t^4+1}dt[/MATH]2. [MATH]= \frac{-1}{(x^2)^4+1}[/MATH] (Fundamental Theorem)
Though this turned out to be wrong, and the correct answer turned out to be [MATH]-\frac{1}{x^8+1}\cdot2x[/MATH]
Can someone please explain to me why my method turned out to be wrong?
I have this question:
Determine[MATH]\frac{d}{dx}\int\limits_{x^2}^0 \frac{1}{t^4+1}dt[/MATH]
My first idea was to solve it through this method:
1. [MATH]=\frac{d}{dx}\int\limits_0^{x^2} \frac{-1}{t^4+1}dt[/MATH]2. [MATH]= \frac{-1}{(x^2)^4+1}[/MATH] (Fundamental Theorem)
Though this turned out to be wrong, and the correct answer turned out to be [MATH]-\frac{1}{x^8+1}\cdot2x[/MATH]
Can someone please explain to me why my method turned out to be wrong?