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Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du, where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably
The light on a lighthouse blinks 45 times a minute. How long will it take the light to blink 405 times? Divide 405 by 45 to get 9 minutes.
Evaluate the subsequent integral. ∫ (tan x/sec 4 x / sec 4 x) dx Solution This kind of integral approximately falls into the form given in 3c. It is a quotient of ta
express the area of a square with sides of length 5ab as monomial
Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary) 1. Map the boundary loop onto a unit rectangle using chord-length
The quotient of 3d 3 and 9d 5 is The key word quotient means division so the problem becomes 1d 3 -5/ 5. Divide the coef?cients: 1d 3 /3d-5 . While dividing like bases, subt
1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent
The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable
how to introduce the topic?
Integrate following. ∫ -2 2 4x 4 - x 2 + 1dx Solution In this case the integrand is even & the interval is accurate so, ∫ -2 2 4x 4 - x 2 + 1dx = 2∫ o
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