How do you do this question?

Step-by-step explanation:

∫₁² [e^(1/x⁴) / x⁵] dx

∫₁² [e^(x⁻⁴) x⁻⁵] dx

If u = x⁻⁴, then du = -4x⁻⁵ dx, and -¼ du = x⁻⁵ dx.

∫ e^u (-¼ du)

-¼ ∫ e^u du

-¼ e^u + C

-¼ e^(x⁻⁴) + C

Evaluate between x=1 and x=2.

-¼ e^(2⁻⁴) − -¼ e^(1⁻⁴)

-¼ e^(1/16) + ¼ e

(e − ¹⁶√e) / 4

Step-by-step explanation:

So we have the definite integral:

Again, we can use u-substitution. Let u equal 1/x^4. So:

Find the derivative:

Divide by -4. So du is:

Of course, we also need to change our bounds. Substitute 1 and 2 into u:

Therefore, our new bounds are from 1 to 1/16.

So, make the substitutions:

The integral of e^u is just e^u. So:

Evaluate for the bounds:

Simplify:

Distribute:

And we're done!

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

step-by-step explanation:

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