If left( int_{0}^{a} x , dx right) le (a + 4) | vedclass

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Question

(B) Given the inequality: $\int_{0}^{a} x \, dx \le a + 4$ Evaluating the definite integral: $\left[ \frac{x^2}{2} \right]_{0}^{a} \le a + 4$ $\frac{a

Vedclass · Accepted Answer

$-2 \le a \le 4$

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(B) Given the inequality: $\int_{0}^{a} x \, dx \le a + 4$ Evaluating the definite integral: $\left[ \frac{x^2}{2} \right]_{0}^{a} \le a + 4$ $\frac{a^2}{2} \le a + 4$ Multiplying by $2$: $a^2 \le 2a + 8$ Rearranging the terms: $a^2 - 2a - 8 \le 0$ Factoring the quadratic expression: $(a - 4)(a + 2) \le 0$ For the product to be less than or equal to zero,$a$ must lie between the roots: $-2 \le a \le 4$.

If $\left( \int_{0}^{a} x \, dx \right) \le (a + 4)$,then

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