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Variable Separable Method

If dy = 4t3...

Question

If $d y = (4 t^{3} + 3 t^{2} + 4 t) d t$ find the value of y.

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Solution

Given that,

$d y = 4 t^{3} + 3 t^{2} + 4 t$

On integrating

$\int d y = \int (4 t^{3} + 3 t^{2} + 4 t) d t$

$y = t^{4} + t^{3} + 2 t^{2}$

Hence, this is the required solution

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Similar questions

y = 1 + t^{4}

x = 3 t^{3} + t

\frac{d y}{d x}

x = {sin}^{- 1} (3 t - {4 t}^{3})

y = {cos}^{- 1} (\sqrt{1 - t^{2}})

\frac{d y}{d x}

y = f (x)

is represented as

x = g (t) = t^{5} - 5 t^{3} - 20 t + 7

y = h (t) = 4 t^{3} - 3 t^{2} - 18 t + 3, (- 2 < t < 2)

f (x)

Q. A function y=f(x) is represented parainetrically as follows:

x = ϕ (t) = t^{5} - 5 t^{3} - 20 t + 7.

y = Ψ (t) = 4 t^{3} - 3 t^{2} - 18 t + 3.

Let the values of "t" at extrema of this function be t1 and t2.Find 2(t1+t2)? Note:

(- 2 < t < 2)

Q. Let the function

y = f (x)

x = t^{5} - 5 t^{3} - 20 t + 7

y = 4 t^{3} - 3 t^{2} - 18 t + 3

t ϵ (- 2, 2)

f^{^{'}} (x)

t = 1

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