I have the following equation :

$${\int}_{0}^{1}\mathrm{cos}(t-\tau )x(\tau )d\tau =t\mathrm{cos}(t)$$

if we replace 1 in the integral for t it is easily solvable using the convolution of Laplace and the answer will be

$$-1+2\mathrm{cos}t$$

I'm studying for a test and have stumbled upon the equation above. Is there any way to solve the equation as it is written , or is it safe to assume its a mistake?

$${\int}_{0}^{1}\mathrm{cos}(t-\tau )x(\tau )d\tau =t\mathrm{cos}(t)$$

if we replace 1 in the integral for t it is easily solvable using the convolution of Laplace and the answer will be

$$-1+2\mathrm{cos}t$$

I'm studying for a test and have stumbled upon the equation above. Is there any way to solve the equation as it is written , or is it safe to assume its a mistake?