Passage: Let k be the area between the curve y= x and x-axis in the interval [0, 4 ] . Question: What is the area between the curve y= x and the x-axis in the interval [ 4 , 2 ] ?

Step-by-step solution

k = ₀^ /4 x , dx Let the required area be A = _ /4 ^ /2 x , dx Substituting x = 2 - t , we get dx = -dt When x = 4 , t = 4 and when x = 2 , t = 0 A = _ /4 ⁰ ( 2 - t ) (-dt) A = ₀^ /4 t , dt A = k Answer: k