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markosheehan
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Find the area bound by the curve y=x^2-16 , the x-axis and the lines x=2 and x=5. i am trying to use the definite integral way ∫_2^5. but i am not getting the right answer. the right answer is 53/3
markosheehan said:Find the area bound by the curve y=x^2-16 , the x-axis and the lines x=2 and x=5. i am trying to use the definite integral way ∫_2^5. but i am not getting the right answer. the right answer is 53/3
The formula for finding the area under a curve is called the definite integral, which is represented by the symbol ∫. It involves taking the antiderivative of the function and evaluating it at two given points, known as the limits of integration.
To find the area under the curve of x^2-16, you will need to first integrate the function to get the antiderivative. In this case, the antiderivative is (1/3)x^3-16x. Then, plug in the two given limits of integration (2 and 5) into this antiderivative and subtract the lower limit from the upper limit to get the area.
The limits of integration represent the starting and ending points on the x-axis where the area under the curve will be calculated. They determine the boundaries of the region whose area is being measured.
No, the method used to find the area under a curve depends on the shape and complexity of the curve. For simple functions like x^2-16, you can use the definite integral. However, for more complicated curves, other methods such as numerical integration may be necessary.
You can visualize the area under a curve by graphing the function and shading the region between the curve and the x-axis. This shaded area represents the numerical value of the definite integral and can help you understand the concept of finding the area under a curve.