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Question: Evaluate the following definite integral: Z 3 1 (2x β 1 + 3 x β 5 x 2 ) dx. (b) Simplify: d dx Z x 5 β2018 cos (t 4 ) dt. (c) Evaluate the following
To write β12 5 - 12 5 as a fraction with a common denominator, multiply by 3 3 3 3. 10 3 β 5 5 β 12 5 β 3 3 10 3 β 5 5 - 12 5 β 3 3. Write each expression with a common denominator of 15 15, by multiplying each by an appropriate factor of 1 1. Tap for more steps 10β 5 15 β 12β 3 15 10 β 5 15 - 12 β 3 15. Combine the
Algebra. Expand Using the Binomial Theorem (1-x)^3. (1 β x)3 ( 1 - x) 3. Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n = n β k=0nCkβ (anβkbk) ( a + b) n = β k = 0 n n C k β ( a n - k b k). 3 β k=0 3! (3β k)!k! β (1)3βk β (βx)k β k = 0 3 3! ( 3 - k)! k! β ( 1) 3 - k β ( - x) k
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