MHT CET · Maths · Continuity and Differentiability
The c.d.f. \(\mathrm{F}(x)\) associated with p.d.f. \(\mathrm{f}(x)\) is
- A (A) \(\quad \mathrm{F}(x)=4 x^3+3 x^4\)
- B \(\mathrm{F}(x)=4 x^3-3 x^4\)
- C \(\mathrm{F}(x)=-4 x^3-3 x^4\)
- D \(\mathrm{F}(x)=-4 x^3+3 x^4\)
Answer & Solution
Correct Answer
(B) \(\mathrm{F}(x)=4 x^3-3 x^4\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \mathrm{F}(x) & =\int_0^x 12 x^2(1-x) \mathrm{d} x \\ & =12 \int_0^x\left(x^2-x^3\right) \mathrm{d} x \\ & =12\left[\frac{x^3}{3}-\frac{x^4}{4}\right]_0^x \\ & =12\left[\frac{x^3}{3}-\frac{x^4}{4}\right] \\ & =4 x^3-3 x^4\end{aligned}\)
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