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Integrate the function $8\sqrt{7+2x^2}x$ from $-3$ to $3$

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The integral of a constant times a function is equal to the constant multiplied by the integral of the function

$8\int_{-3}^{3}\sqrt{7+2x^2}xdx$

Learn how to solve differential calculus problems step by step online.

$8\int_{-3}^{3}\sqrt{7+2x^2}xdx$

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Learn how to solve differential calculus problems step by step online. Integrate the function (7+2x^2)^1/28x from -3 to 3. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. First, factor the terms inside the radical by 2 for an easier handling. Taking the constant out of the radical. We can solve the integral \int\sqrt{2}\sqrt{\frac{7}{2}+x^2}xdx by applying integration method of trigonometric substitution using the substitution.

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve integral of (7+2x^2)^0.58dx from -3 to 3 using partial fractionsSolve integral of (7+2x^2)^0.58dx from -3 to 3 using basic integralsSolve integral of (7+2x^2)^0.58dx from -3 to 3 using u-substitutionSolve integral of (7+2x^2)^0.58dx from -3 to 3 using integration by partsSolve integral of (7+2x^2)^0.58dx from -3 to 3 using trigonometric substitution

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Function Plot

Plotting: $8\sqrt{7+2x^2}x$

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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