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

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.