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cabellos
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I just need a check on when integrating sin(xy) with respect to x? Does this become -cos(xy) or -cos(x)
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Integrating with respect to x means finding the area under a curve in the x-direction. It involves adding up all the infinitely small rectangles that make up the curve.
The main difference is the direction in which the area is being measured. Integrating with respect to x measures the area in the x-direction, while integrating with respect to y measures the area in the y-direction.
Integrating with respect to x is used to solve problems involving rates of change, such as finding the distance traveled by an object with varying velocity or the volume of a three-dimensional shape with varying cross-sectional area.
Integration with respect to x is the inverse operation of differentiation, which is finding the rate of change of a function. Integration allows us to recover the original function from its derivative by finding the area under the curve of the derivative.
Integrating with respect to x has many real-life applications, such as in physics, engineering, economics, and statistics. It is used to solve problems involving rates of change and to find areas, volumes, and averages in various contexts.