∫0axsin((3∗22/7)x/a)sin(22x/7a)dx\int_{0}^{a}x sin((3*22/7)x/a) sin (22x/7a) dx

asked by guest
on Mar 13, 2025 at 11:45 am



You asked:

Evaluate the integral: ∫0axsin⁡(3⋅227xa)sin⁡(22x7a)dx\int_{0}^{a}{x \sin\left( \frac{\frac{3 \cdot 22}{7} x}{a} \right) \sin\left( \frac{22 x}{7 a} \right)}dx

MathBot Answer:

∫0axsin⁡(3⋅227xa)sin⁡(22x7a)dx=−147a215488−21a2sin⁡(227)cos⁡(667)176+245a2sin⁡(227)sin⁡(667)15488+7a2sin⁡(667)cos⁡(227)176+147a2cos⁡(227)cos⁡(667)15488\int_{0}^{a}{x \sin\left( \frac{\frac{3 \cdot 22}{7} x}{a} \right) \sin\left( \frac{22 x}{7 a} \right)}dx = - \frac{147 a^{2}}{15488} - \frac{21 a^{2} \sin{\left(\frac{22}{7} \right)} \cos{\left(\frac{66}{7} \right)}}{176} + \frac{245 a^{2} \sin{\left(\frac{22}{7} \right)} \sin{\left(\frac{66}{7} \right)}}{15488} + \frac{7 a^{2} \sin{\left(\frac{66}{7} \right)} \cos{\left(\frac{22}{7} \right)}}{176} + \frac{147 a^{2} \cos{\left(\frac{22}{7} \right)} \cos{\left(\frac{66}{7} \right)}}{15488}

+ Submit Question