Problem 50
Football Teams A football squad has 7 linemen, 11 linebackers, and 9 safeties. How many different teams composed of 5 linemen, 3 linebackers, and 3 safeties can be formed?
Step-by-Step Solution:
Integrating any rational function Ratio of polynomials: by expressing the function 3 2 2 x −1 = (x−1)(x +1) = x(x−1) (+−1)(x +1) x −1 x(x +1) x(x +1) x(x +1) x−1 x−1 x 1 1 ¿ 2 + = 2 − 2 +1− x +1 x x +1 x +1 x Decompose any rational function P(x) R(x)= =G x)+ f1x)+ f2x +… f kx) Q( ) f (x) A Bx+c i {(ax+b ) (p x +qx+r)m} Example 3 2 x +x +x−1 ∫ 2 x +2 x+2 Step 1 if numerator is of higher degree than denominator Long division Multiple everything by x here x+1 ∫ xdx−∫dx+ ∫ 2 x +2x+2 2 letu=x +2x+2 du= 2x+2 )dx 1 du= (+1 d) 2
Step 2 of 1
