Integration with U Substitution

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What is u-substitution in integration?

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U-substitution is a method used to simplify the process of integration by substituting a part of the integrand with a new variable (u), making the integral easier to solve.

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What is the formula for u-substitution?

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If u = g(x), then dx = (1/g'(x)) du, and the integral becomes \int f(g(x)) g'(x) dx = \int f(u) du.

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The answer is 26.

Front

What does the derivative d'(t) represent in motion problems?

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d'(t) represents the velocity of an object at time t.

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When is an object moving to the left in terms of velocity?

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An object is moving to the left when its velocity is negative.

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What is the relationship between the integral and the area under the curve?

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The definite integral of a function over an interval gives the net area between the curve and the x-axis over that interval.

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What is the Fundamental Theorem of Calculus?

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What is the purpose of definite integrals?

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Definite integrals are used to calculate the total accumulation of a quantity, such as area, volume, or displacement, over a specific interval.