JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\sum_{ r =1}^{20}\left(\left|\sqrt{\pi\left(\int_0^{ r } x \mid \sin \pi x dx \right)}\right|\right)\) is ___ .
- A 200
- B 210
- C 190
- D 220
Answer & Solution
Correct Answer
(B) 210
Step-by-step Solution
Detailed explanation
Let \(I_r=\int_0^r x|\sin \pi x| d x\) ...(1) Apply King Property \(=\int_0^{\mathrm{r}}(\mathrm{r}-\mathrm{x})|\sin \pi \mathrm{x}| \mathrm{dx}\) ... (2) By (1) + (2) \(2 I_r=\int_0^r r|\sin \pi x| d x \Rightarrow I_r=\frac{r}{2} \int_0^r|\sin \pi x| d x\)…
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