1. Tardigrade
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  3. Mathematics
  4. If y=∫ limitsu(x)v(x) f(t) d t, let us define (d y/d x) in a different manner as (d y/d x)=v prime(x) f2(v(x))-u prime(x) f2(u(x)) and the equation of the tangent at (a, b) as y-b=((d y/d x))(a, b)(x-a) If y=∫ limitsxx2 t2 d t, then equation of tangent at x=1 is

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Q. If $y=\int\limits_{u(x)}^{v(x)} f(t) d t$, let us define $\frac{d y}{d x}$ in a different manner as $\frac{d y}{d x}=v^{\prime}(x) f^2(v(x))-u^{\prime}(x) f^2(u(x))$ and the equation of the tangent at $(a, b)$ as $y-b=\left(\frac{d y}{d x}\right)_{(a, b)}(x-a)$
If $y=\int\limits_x^{x^2} t^2 d t$, then equation of tangent at $x=1$ is

Integrals

Solution:

At $x=1, y=0$
$\frac{d y}{d x}=2 x \cdot x^8-x^4=2-1=1$
$\therefore $ equation of tangent $y-0=1(x-1)$
$ y=x-1$