ExamBro
ExamBro
AP EAMCET · Maths · Indefinite Integration

If \(\int_1^n[x] d x=120\), then \(n=\)

  1. A 15
  2. B 16
  3. C 14
  4. D 12
Verified Solution

Answer & Solution

Correct Answer

(B) 16

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \mathrm{I}=\int_1^n[x] d x=120 \\ & \int_1^2 1 d x+\int_2^3 2 d x+\int_3^4 3 d x+\ldots+\int_{n-1}^n(n-1) d x=120 \\ & \Rightarrow 1+2+\ldots+n-1=120 \Rightarrow \frac{(n-1) n}{2}=120 \\ & \Rightarrow n=16,-15 \text { (rejected) } \Rightarrow…