# Big Problem but, Small solution!!

Calculus Level 4

Let $$f$$ be a function on $$\mathbb{R} \to \mathbb{R}$$such that $$f(1) = 1$$. If the y-intercept of the tangent at any point $$\text{P}(x,y)$$ on curve $$y = f(x)$$ is equal to the cube of abcissa of $$\text{P}$$. Then find $$f(-3)$$.

And now if ,$\displaystyle\int_{0}^{ f(-3) - 9} 4 \cos\frac{x}{2} . \cos{x} . \sin\frac{21x}{2} dx = \text{k}$

Find the value of $$\text{k} + 0.111$$

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