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Find the following definite integral. int_(-1)^(0)2xdx

Find the following definite integral.\newline∫−102xdx \int_{-1}^{0} 2 x d x

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Full solution

Q. Find the following definite integral.\newline∫−102xdx \int_{-1}^{0} 2 x d x
  1. Calculate antiderivative: Calculate the integral of 2x2x from −1-1 to 00. To solve ∫−102x dx\int_{-1}^{0} 2x \, dx, we start by finding the antiderivative of 2x2x, which is x2x^2.
  2. Evaluate at limits: Evaluate the antiderivative at the upper and lower limits and subtract.\newlinePlug in the limits into x2x^2:\newlineAt x=0x = 0, x2=02=0x^2 = 0^2 = 0.\newlineAt x=−1x = -1, x2=(−1)2=1x^2 = (-1)^2 = 1.\newlineNow, subtract the lower limit evaluation from the upper limit evaluation: 0−1=−10 - 1 = -1.

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