red Trigonometric Substitution The integral a t dt represents the area under the curve y =...

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red Trigonometric Substitution The integral a t dt represents the area under the curve y = a - +2 between the vertical lines t = 0 and t = x. Notice that there are two regions: a triangular region and a sector of the circle t + y = a in the blue. y y = a 2 Using the picture on the left write a formula the areas (no calculus needed) The triangular region x The sector in terms of x. Recall the area of a sector is (radius squared times central angle) Use trigonometric substitution to show that a - t dt = a sin (2) + a x red Trigonometric Substitution The integral a t dt represents the area under the curve y = a - +2 between the vertical lines t = 0 and t = x. Notice that there are two regions: a triangular region and a sector of the circle t + y = a in the blue. y y = a 2 Using the picture on the left write a formula the areas (no calculus needed) The triangular region x The sector in terms of x. Recall the area of a sector is (radius squared times central angle) Use trigonometric substitution to show that a - t dt = a sin (2) + a x