How do you find the definite integral of #int (1-2x-3x^2)dx# from #[0,2]#?

Answer 1

#int_0^2(1-2x-3x^2)d x=-10#

#int_0^2(1-2x-3x^2)d x=|x-2*1/2*x^2-3*1/3*x^3|_0^2# #int_0^2(1-2x-3x^2)d x=|x-x^2-x^3|_0^2# #int_0^2(1-2x-3x^2)d x=2-2^2-2^3# #int_0^2(1-2x-3x^2)d x=2-4-8# #int_0^2(1-2x-3x^2)d x# #int_0^2(1-2x-3x^2)d x=-10#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the definite integral of ( \int (1 - 2x - 3x^2) , dx ) from ( x = 0 ) to ( x = 2 ), you first need to integrate the function with respect to ( x ), then evaluate the result at the upper and lower limits of integration (in this case, 2 and 0 respectively), and finally subtract the result at the lower limit from the result at the upper limit.

First, integrate the function: [ \int (1 - 2x - 3x^2) , dx = \left( x - x^2 - x^3 \right) + C ]

Next, evaluate the antiderivative at the upper and lower limits: [ F(2) = \left( 2 - 2^2 - 2^3 \right) = -6 ] [ F(0) = \left( 0 - 0^2 - 0^3 \right) = 0 ]

Finally, subtract the result at the lower limit from the result at the upper limit: [ F(2) - F(0) = -6 - 0 = -6 ]

So, the definite integral of ( \int (1 - 2x - 3x^2) , dx ) from ( x = 0 ) to ( x = 2 ) is ( -6 ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7