$\"\"$

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The equation $\"\"$ .

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The function is $\"\"$ .

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Apply integral on each side on interval $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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By the Mean Value Theorem for Integrals:

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If $\"\"$ is continuous on the closed interval $\"\"$ , then there exists a number in $\"\"$ in the closed interval $\"\"$ such that $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$ .

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Therefore, the function $\"\"$ has atleast one real zero.

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$\"\"$

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The function $\"\"$ has atleast one real zero.