Even and Odd SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd

Term-102 Even and Odd

Term-102 Even and Odd

Term-091 Even and Odd

Term-102 Even and Odd

Term-103 Even and Odd

SYMMETRY Suppose f is continuous on [-a, a] and even Suppose f is continuous on [-a, a] and odd Example Even and Odd

AREAS BETWEEN CURVES Area between two curves

AREAS BETWEEN CURVES Area between two curves Find the area of the region bounded by the curves and Example: Both right-hand and left- hand boundary are lines Note:

AREAS BETWEEN CURVES Area between two curves Both right-hand and left- hand boundary reduce to a point Note:

AREAS BETWEEN CURVES Area between two curves The value of a and b (not given) Note: Steps: 1) Find the intersection points 2) Write the area as an integral

AREAS BETWEEN CURVES Area between two curves

THE SUBSTITUTION RULE T-092

THE SUBSTITUTION RULE T-102

AREAS BETWEEN CURVES

Area between two curves Some regions are best treated by regarding x as a function of y.

AREAS BETWEEN CURVES Area between two curves Some regions are best treated by regarding x as a function of y.

AREAS BETWEEN CURVES Steps: 1) Rewrite the function as x in terms of y 2) Find the intersection points

AREAS BETWEEN CURVES We could have found the area in by integrating with respect to x instead of y, but the calculation is much more involved.

AREAS BETWEEN CURVES T-092

AREAS BETWEEN CURVES