Let f x = max x + 1 , x + 2 , … , x + 5 . Then ∫ - 6 0 f x d x is equal to ______.

Let fx=maxx+1,x+2,…,x+5. Then ∫-60fxdx is equal to ______.

Solution

fx= max x+1,x+2,x+3,x+4,x+5

 

∫-60fxdx=∫-6-3x+1dx+∫-30x+5dx

=-∫-6-3x+1dx+∫-30x+5dx

=-x22+x-6-3+x22+5x-30

=-92-3-18-6+0-92-15

=-32-12+212=212+212=21

Asked in: JEE Main 2022 (26 Jun Shift 1)

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