Find the area under the curve y=X+1 between X=0 to X= 3
To find the area under the curve y = x + 1 between x = 0 and x = 3, first we need to integrate the function with respect to x:
∫(x + 1) dx = (1/2)x^2 + x + C
Now we can find the area under the curve by evaluating the integral at x = 0 and x = 3:
Area = [(1/2)(3)^2 + 3] - [(1/2)(0)^2 + 0]
Area = [(1/2)(9) + 3] - 0
Area = (9/2 + 3) - 0
Area = (9/2 + 6)/2
Area = 15/2
Area = 7.5
Therefore, the area under the curve y = x + 1 between x = 0 and x = 3 is 7.5 square units.