How do you calculate the value of the integral #inte^(4t²-t) dt# from #[3,x]#?

Answer 1

That integral cannot be expressed using elementary functions. If requires the use of #int e^(x^2) dx#. However the derivative of the integral is #e^(4x^2-x)#

The fundamental theorem pf calculus part 1 tells us that the derivative with respect to #x# of:
#g(x) = int_a^x f(t) dt# is #f(x)#
So the derivative (with respect to #x#) of
#g(x) = int_3^x e^(4t^2-t) dt" "# is #" "g'(x) = e^(4x^2 -x)#.
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Answer 2

#inte^(4t^2-t)dt=(e^(4x^2-x))/(8x-1)-e^(33)/23#

Be #f(x)=e^(4t^2-t)# your function.
In order to integrate this function, you will need its primitive #F(x)#
#F(x)=(e^(4t^2-t))/(8t-1)+k# with #k# a constant.
The integration of #e^(4t^2-t)# on [3;x] is calculated as follows:
#inte^(4t^2-t)dt=F(x)-F(3)#
#=(e^(4x^2-x))/(8x-1)+k-((e^(4cdot3^2-3))/(8cdot3-1)+k)#
#=(e^(4x^2-x))/(8x-1)-e^(33)/23#
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Answer 3

To calculate the value of the integral ∫e^(4t²-t) dt from [3,x], you first need to find the antiderivative of e^(4t²-t) with respect to t. Then, you evaluate this antiderivative at the upper bound x and subtract the value of the antiderivative at the lower bound 3. The result gives you the value of the integral from 3 to x.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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