Give an expression for p(x) so the integral can be evaluated useing substitution do not evaluate. intergal p(x)e^x^4 dx

4x^3

Step-by-step explanation:

Choose p so that it's the derivative of x^4.

This would give us integral(e^u du) which is integratable over elementary functionssimply it is e^u+c.

Anyways, p=(x^4)' which gives 4x^3 by power rule.

Choose p(x)=4x^3 or a constant multiple of this would also suffice.

21

step-by-step explanation:

11279

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.