Evaluate the integral integral from nothing to nothing ∫ startfraction 3 over t superscript 4 endfraction 3 t4 sine left parenthesis startfraction 1 over t cubed endfraction minus 6 right parenthesis sin 1 t3 −6dt

Step-by-step explanation:

Given  function:

Now,

let be 'x'

Therefore,

= dx

or

= dx

on substituting the above values in the equation, we get

⇒ ∫ - sin (x) . dx

or

⇒ cos (x) + c                      [ ∵ ∫sin (x) . dx = - cos (x)]

Here,

c is the integral constant

on substituting the value of 'x' in the equation, we get

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

the number of the people going.

step-by-step explanation:

the cost to buy one movie ticket is $7. if the total cost for the movie is a function of how many people go, then the input is : the number of the people going.