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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

$-2 \le a \le 4$

Vedclass · Answer

(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

Similar Questions

If $\int_0^1 {x \log \left( {1 + \frac{x}{2}} \right)} \,dx = a + b \log \frac{2}{3},$ then

$\int_1^4 \left(x + \sqrt{x} + \frac{1}{x}\right) dx - \int_1^{2 \log 2} dx = $

$\int_{2}^{4} (|x - 2| + |x - 3|) dx =$

$\int_0^\pi |\cos x| \, dx = $

$\int_0^1 (0.001)^{\frac{x}{3}} e^x \, dx =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module