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How do you find the integral #( x^4 - 3x^3 + 6x^2 - 7 ) dx#?

Answer 1

Christopher Allers

Have a look:

hope it helps!

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Answer 2

Emily Ammerman

by definition, we know that #intx^ndx=(x^(n+1))/(n+1)#

Thus,

#int(x^4-3x^3+6x^2-7)dx=(x^5)/5-(3x^4)/4+2x^3-7x+c#

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Answer 3

Charles Anctil

To find the integral of ( x^4 - 3x^3 + 6x^2 - 7 ) with respect to ( x ), you can use the power rule of integration:

[ \int x^n , dx = \frac{x^{n+1}}{n+1} + C ]

Applying this rule to each term of the polynomial:

[ \int (x^4 - 3x^3 + 6x^2 - 7) , dx = \frac{x^5}{5} - \frac{3x^4}{4} + \frac{6x^3}{3} - 7x + C ]

[ = \frac{x^5}{5} - \frac{3x^4}{4} + 2x^3 - 7x + C ]

Where ( C ) is the constant of integration.

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Answer 4

Isaiah Allen

To find the integral of x^4 - 3x^3 + 6x^2 - 7 with respect to x, you can use the power rule for integration. The result is (1/5)x^5 - (3/4)x^4 + (6/3)x^3 - 7x + C, where C is the constant of integration.

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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.