**Topic: Calculus - Numerical Integration Techniques****Objective:** Find \( L_n \), \( R_n \), and their average for the definite integral below using the indicated value of \( n \).**Definite Integral:**\[ \int_{1}^{5} (x^2 + 4) \, dx, \quad n = 4\]**Explanation:**In this problem, you are asked to approximate the definite integral of the function \( x^2 + 4 \) from 1 to 5 using numerical methods. The methods involved are the Left Riemann Sum (\( L_n \)), Right Riemann Sum (\( R_n \)), and the average of these two values.- **Left Riemann Sum (\( L_n \))**: This method approximates the area under the curve by using the left endpoints of subintervals. For \( n = 4 \), we divide the interval [1, 5] into 4 equal subintervals and calculate the sum of areas of rectangles using the left endpoints.- **Right Riemann Sum (\( R_n \))**: This method uses the right endpoints of subintervals to approximate the integral. Similarly, divide the interval [1, 5] into 4 equal subintervals and compute the rectangle areas using the right endpoints.- **Average of \( L_n \) and \( R_n \)**: After calculating both sums, take their average to obtain a more accurate approximation of the integral.This approach is useful for understanding how numerical methods can approximate integrals when an analytical solution is difficult to obtain or when dealing with real-world data.

Given integral:- ∫15x2+4dx∆x=5-14=1 Endpoints 1,2,3,4,5 fx=x2+4 ⇒fx0=f1=12+4=5 ⇒fx1=f2=22+4=8 ⇒fx2=f3=32+4=13 ⇒fx3=f4=42+4=20 ⇒fx4=f5=52+4=29 Ln=∆xfx0+fx1+fx2......+fxn-2+fxn-1 ⇒L4=∆xfx0+fx1+fx2+fx3 ⇒L4=15+8+13+20 ⇒L4=46 Rn=∆xfx1+fx2......+fxn-2+fxn-1+fxn ⇒R4=∆xfx1+fx2+fx3+fx4 ⇒R4=18+13+20+29 ⇒R4=70 ⇒Average =L4+Rn2 ⇒Average =46+702=58Hence Ln=46 ,Rn=70 Average=58